Volume - Pre-Algebra
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The volume of a cone whose height is three times the radius of its base is one cubic yard. Give its radius in inches.
The volume of a cone whose height is three times the radius of its base is one cubic yard. Give its radius in inches.
The volume of a cone with base radius
and height
is

The height
is three times this, or
. Therefore, the formula becomes


Set this volume equal to one and solve for
:



![r=\sqrt[3]{\frac{ 1 }{ \pi}} ={\frac{ \sqrt[3] {1} }{ \sqrt[3]{ \pi}}} ={\frac{ 1}{ \sqrt[3]{ \pi}}}={\frac{1 \cdot \sqrt[3]{ \pi^{2} }}{ \sqrt[3]{ \pi} \cdot \sqrt[3]{ \pi^{2}}} ={\frac{ \sqrt[3]{ \pi^{2} }}{ \pi}}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/204806/gif.latex)
This is the radius in yards; since the radius in inches is requested, multiply by 36.
![\frac{ \sqrt[3]{ \pi^{2} }}{ \pi} \times 36 = \frac{ 36 \sqrt[3]{ \pi^{2} }}{ \pi}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/204807/gif.latex)
The volume of a cone with base radius and height
is
The height is three times this, or
. Therefore, the formula becomes
Set this volume equal to one and solve for :
This is the radius in yards; since the radius in inches is requested, multiply by 36.
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Which of the following is the volume of the above cone?
Which of the following is the volume of the above cone?
The volume of a cone whose height is
and whose base has radius
is defined by the formula
.
Set
:



cubic centimeters.
The volume of a cone whose height is and whose base has radius
is defined by the formula
.
Set :
cubic centimeters.
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The standard waffle cone at Cream Canyon Ice Cream Parlor has a diameter of 4 inches. If the height of the cone is 1.5 times the diameter, what is the volume of the cone?
The standard waffle cone at Cream Canyon Ice Cream Parlor has a diameter of 4 inches. If the height of the cone is 1.5 times the diameter, what is the volume of the cone?
We must first recall the formula for the volume of a cone.

where
is the radius and
is the height. The problem is that we are not provided with either the height or the radius. However, we are told that the height is 1.5 times the diameter. Since the diameter is 4 inches, we can calculate
. Thus the height of the cone is 6 inches. We must also recall that the radius of a circle (such as the top of an ice cream cone) is simply half the diameter. Therefore, if the diameter is 4 inches, the radius is 2 inches. We now have all of the essential ingredients for volume.

Since our measurements were all in inches, our volume will be in cubic inches. Therefore, the volume of our ice cream cone is
. Now all we need is a scoop or two of our favorite flavor.
We must first recall the formula for the volume of a cone.
where is the radius and
is the height. The problem is that we are not provided with either the height or the radius. However, we are told that the height is 1.5 times the diameter. Since the diameter is 4 inches, we can calculate
. Thus the height of the cone is 6 inches. We must also recall that the radius of a circle (such as the top of an ice cream cone) is simply half the diameter. Therefore, if the diameter is 4 inches, the radius is 2 inches. We now have all of the essential ingredients for volume.
Since our measurements were all in inches, our volume will be in cubic inches. Therefore, the volume of our ice cream cone is . Now all we need is a scoop or two of our favorite flavor.
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What is the volume of a cone with a radius of two and a height of three?
What is the volume of a cone with a radius of two and a height of three?
Write the formula to find the volume of the cone.

Substitute the radius and height.

Write the formula to find the volume of the cone.
Substitute the radius and height.
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What is the volume of a cone with a radius of 5 and a height of 6?
What is the volume of a cone with a radius of 5 and a height of 6?
Write the formula to find the volume of a cone.

Substitute the dimensions and solve.

Write the formula to find the volume of a cone.
Substitute the dimensions and solve.
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Find the volume of a cone with a base area of
and a height of
.
Find the volume of a cone with a base area of and a height of
.
The base of a cone has a circular cross section. Given the base area, there is no need to determine the radius.
Write the formula for the volume of a cone.

The
term represents the base area of the circle.
Substitute all the given values into the volume formula.

The base of a cone has a circular cross section. Given the base area, there is no need to determine the radius.
Write the formula for the volume of a cone.
The term represents the base area of the circle.
Substitute all the given values into the volume formula.
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What is the volume of a cone with diameter of 2 and a height of 10?
What is the volume of a cone with diameter of 2 and a height of 10?
Write the formula for the volume of a cone.

The radius is half the diameter.
Substitute the radius and the height.

Write the formula for the volume of a cone.
The radius is half the diameter.
Substitute the radius and the height.
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Find the volume of a cone with a radius of
and a height of
.
Find the volume of a cone with a radius of and a height of
.
Write the volume formula for a cone.

Substitute the dimensions.

Write the volume formula for a cone.
Substitute the dimensions.
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Find the volume of the cone that has a radius of
and a height of
.
Find the volume of the cone that has a radius of and a height of
.
Write the formula to find the volume of a cone.


Write the formula to find the volume of a cone.
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Find the volume of a cone with a radius of
and a height of
.
Find the volume of a cone with a radius of and a height of
.
Write the formula to find the volume of the vone.

Substitute the dimensions into the formula.

Expand the terms.

Multiply the integers for the volume.

Write the formula to find the volume of the vone.
Substitute the dimensions into the formula.
Expand the terms.
Multiply the integers for the volume.
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Solve for the volume of a cone with a circular area of
and a height of
.
Solve for the volume of a cone with a circular area of and a height of
.
Write the formula for the volume of a cone.

The area of the circular base is represented as
in the equation.
Substitute
in replacement of this term. Substitute the height into the volume formula as well.

Multiply out each term and leave
as is.

Write the formula for the volume of a cone.
The area of the circular base is represented as in the equation.
Substitute in replacement of this term. Substitute the height into the volume formula as well.
Multiply out each term and leave as is.
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You have an ice cream cone. You want to fill the cone completely with ice cream. What is the volume of ice cream you can fill it with if the height of the cone is 12cm and the diameter is 8cm?
You have an ice cream cone. You want to fill the cone completely with ice cream. What is the volume of ice cream you can fill it with if the height of the cone is 12cm and the diameter is 8cm?
The formula to find the volume of a cone is

where r is the radius and h is the height. We know the diameter of the ice cream cone is 8cm. We also know the radius is half the diameter, so the radius is 4cm. We know the height is 12cm. Using substitution, we get




The formula to find the volume of a cone is
where r is the radius and h is the height. We know the diameter of the ice cream cone is 8cm. We also know the radius is half the diameter, so the radius is 4cm. We know the height is 12cm. Using substitution, we get
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What is the volume of a cylinder with a diameter equal to
and height equal to
?
What is the volume of a cylinder with a diameter equal to and height equal to
?
If the diameter is 6, then the radius is half of 6, or 3.
Plug this radius into the formula for the volume of a cylinder:

If the diameter is 6, then the radius is half of 6, or 3.
Plug this radius into the formula for the volume of a cylinder:
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Find the volume of the cylinder.
Jared buys a can of chicken noodle soup for dinner. The height of the can is
. The radius of the can is
. What is the volume of the can?
Find the volume of the cylinder.
Jared buys a can of chicken noodle soup for dinner. The height of the can is . The radius of the can is
. What is the volume of the can?
The correct answer to the question is
.
We know that a can is a cylinder. We also know that the formula for the volume of a cylinder is
.
Plug in the numbers we are given:

Once we multiply these numbers, we get
.
The unit for our answer is
since we are solving a volume problem.
The correct answer to the question is .
We know that a can is a cylinder. We also know that the formula for the volume of a cylinder is .
Plug in the numbers we are given:
Once we multiply these numbers, we get .
The unit for our answer is since we are solving a volume problem.
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A cylinder has a radius of 4 inches and a height of 5 inches. What is the volume of the cylinder?
A cylinder has a radius of 4 inches and a height of 5 inches. What is the volume of the cylinder?
The formula for the volume of the cylinder is
, where
is the radius and
is the height. Plug in the lengths we are given to solve:




The cylinder has a volume of
.
The formula for the volume of the cylinder is , where
is the radius and
is the height. Plug in the lengths we are given to solve:
The cylinder has a volume of .
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What is the volume of a cylinder with a height of 20 and a radius of 10?
What is the volume of a cylinder with a height of 20 and a radius of 10?
The volume of a cylinder is given by the formula:

with
and
, the equation is:
,
Thus,
, or 
The volume of a cylinder is given by the formula:
with and
, the equation is:
,
Thus, , or
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Find the volume of a cylinder that has a radius of 2 inches and a height of 10 inches.

Find the volume of a cylinder that has a radius of 2 inches and a height of 10 inches.
Radius = 2 Inches
Height = 10




Radius = 2 Inches
Height = 10
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If Cindy has a cylindrical bucket filled with sand, how much sand does it contain if area of the circular bottom is
inches and the heigh of the bucket is
inches?
If Cindy has a cylindrical bucket filled with sand, how much sand does it contain if area of the circular bottom is inches and the heigh of the bucket is
inches?
To find the volume of a cylinder, the formula is
.
Normally, you would simply input the radius given for "
" and the height given for "
". However, the question did not directly give us the radius; it gave us the area of the circular bottom.
Now examine the volume formula closely, and you will see that the formula for the area of a circle is hidden inside the volume formula. If
is the area of a circle, then we can simply multiply the area of the circle given by the height given.
V = area of the circle x height

cubed inches
To find the volume of a cylinder, the formula is .
Normally, you would simply input the radius given for "" and the height given for "
". However, the question did not directly give us the radius; it gave us the area of the circular bottom.
Now examine the volume formula closely, and you will see that the formula for the area of a circle is hidden inside the volume formula. If is the area of a circle, then we can simply multiply the area of the circle given by the height given.
V = area of the circle x height
cubed inches
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Find the volume of a cylinder with a diameter of 1 and a height of 2.
Find the volume of a cylinder with a diameter of 1 and a height of 2.
Write the formula for the volume of a cylinder.

Find the radius by dividing the diameter by 2.


Write the formula for the volume of a cylinder.
Find the radius by dividing the diameter by 2.
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The area of the circular base of a cylinder is
. The height of the cylinder is
. What is the volume of the cylinder?
The area of the circular base of a cylinder is . The height of the cylinder is
. What is the volume of the cylinder?
Write the formula to find the volume of the cylinder.

The
term represents the area of the circular base. Multiply the given area and the height to obtain the area.

Write the formula to find the volume of the cylinder.
The term represents the area of the circular base. Multiply the given area and the height to obtain the area.
Compare your answer with the correct one above