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Example Questions
Example Question #1 : How To Find The Surface Area Of A Cone
What is the surface area of a cone with a radius of 6 in and a height of 8 in?
66π in2
112π in2
60π in2
96π in2
36π in2
96π in2
Find the slant height of the cone using the Pythagorean theorem: r2 + h2 = s2 resulting in 62 + 82 = s2 leading to s2 = 100 or s = 10 in
SA = πrs + πr2 = π(6)(10) + π(6)2 = 60π + 36π = 96π in2
60π in2 is the area of the cone without the base.
36π in2 is the area of the base only.
Example Question #1041 : Act Math
Use the following formula to answer the question.
The slant height of a right circular cone is . The radius is
, and the height is
. Determine the surface area of the cone.
Notice that the height of the cone is not needed to answer this question and is simply extraneous information. We are told that the radius is , and the slant height is
.
First plug these numbers into the equation provided.
Then simplify by combining like terms.
Example Question #1 : How To Find The Surface Area Of A Cone
The slant height of a cone is ; the diameter of its base is one-fifth its slant height. Give the surface area of the cone in terms of
.
The formula for the surface area of a cone with base of radius and slant height
is
.
The diameter of the base is ; the radius is half this, so
Substitute in the surface area formula:
Example Question #1 : How To Find The Surface Area Of A Cone
The radius of the base of a cone is ; its slant height is two-thirds of the diameter of that base. Give its surface area in terms of
.
The formula for the surface area of a cone with base of radius and slant height
is
.
The diameter of the base is twice radius , or
, and its slant height is two-thirds of this diameter, which is
. Substitute this for
in the formula:
Example Question #771 : Geometry
The radius of the base of a cone is ; its height is twice of the diameter of that base. Give its surface area in terms of
.
The formula for the surface area of a cone with base of radius and slant height
is
.
The base has radius and diameter
. The height is twice the diamter, which is
. Its slant height can be calculated using the Pythagorean Theorem:
Substitute for
in the surface area formula:
Example Question #1 : How To Find The Surface Area Of A Cone
The height of a cone is ; the diameter of its base is twice the height. Give its surface area in terms of
.
The formula for the surface area of a cone with base of radius and slant height
is
.
The diameter of the base is twice the height, which is ; the radius is half this, which is
.
The slant height can be calculated using the Pythagorean Theorem:
Substitute for
and
for
in the surface area formula:
Example Question #1 : How To Find The Surface Area Of A Cone
The circumference of the base of a cone is 80; the slant height of the cone is equal to twice the diameter of the base. Give the surface area of the cone (nearest whole number).
The formula for the surface area of a cone with base of radius and slant height
is
.
The slant height is twice the diameter, or, equivalently, four times the radius, so
and
The radius of the base is the circumference divided by , which is
Substitute:
Example Question #21 : Advanced Geometry
The circumference of the base of a cone is 100; the height of the cone is equal to the diameter of the base. Give the surface area of the cone (nearest whole number).
The formula for the surface area of a cone with base of radius and slant height
is
.
The diameter of the base is the circumference divided by , which is
This is also the height .
The radius is half this, or
The slant height can be found by way of the Pythagorean Theorem:
Substitute in the surface area formula:
Example Question #1 : How To Find The Surface Area Of A Cone
A heat shield on a particular satellite takes the form of a cone. If the surface area of the "face" of the cone (not counting the disk on the bottom) is , and the stripe of reflective paint from the tip of the cone is down to the base is
feet long, what is the diameter of the disk in feet? Round
to 3 significant digits. Round your final answer to the nearest foot.
In this problem, we only need to consider the part of the formula for conic surface area that deals with slant height, since that is all the information we have.
We know the formula for the lateral surface area of a cone is , and we know that
is
feet. Plugging in our other values gives us:
Simplify:
Thus, if our radius is approximately feet, our diameter is approximately
feet.
Example Question #2 : How To Find The Surface Area Of A Cone
What is the surface area in square units of a cone with radius units and height
units?
The formula for surface area of a cone is:
, where
is the slant height. Since we know the radius, we can calculate the first part without issue:
The second part requires us to calculate slant height. Since all cones have a right angle created by the base and height perpendicular to the base, we can use the Pythagorean theorem to calculate :
Now, we can complete our formula. Don't forget to add in the circular base.
Thus, our surface area is square units.
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