All SSAT Upper Level Math Resources
Example Questions
Example Question #622 : Geometry
Chestnut wood has a density of about . A right circular cone made out of chestnut wood has a height of three meters, and a base with a radius of two meters. What is its mass in kilograms (nearest whole kilogram)?
First, convert the dimensions to cubic centimeters by multiplying by : the cone has height , and its base has radius .
Its volume is found by using the formula and the converted height and radius.
Now multiply this by to get the mass.
Finally, convert the answer to kilograms.
Example Question #1 : How To Find The Volume Of A Cone
A cone has the height of 4 meters and the circular base area of 4 square meters. If we want to fill out the cone with water (density = ), what is the mass of required water (nearest whole kilogram)?
6333
The volume of a cone is:
where is the radius of the circular base, and is the height (the perpendicular distance from the base to the vertex).
As the circular base area is , so we can rewrite the volume formula as follows:
where is the circular base area and known in this problem. So we can write:
We know that density is defined as mass per unit volume or:
Where is the density; is the mass and is the volume. So we get:
Example Question #623 : Geometry
The vertical height (or altitude) of a right cone is . The radius of the circular base of the cone is . Find the volume of the cone in terms of .
The volume of a cone is:
where is the radius of the circular base, and is the height (the perpendicular distance from the base to the vertex).
Example Question #624 : Geometry
A right cone has a volume of , a height of and a radius of the circular base of . Find .
The volume of a cone is given by:
where is the radius of the circular base, and is the height; the perpendicular distance from the base to the vertex. Substitute the known values in the formula:
Example Question #4 : How To Find The Volume Of A Cone
A cone has a diameter of and a height of . In cubic meters, what is the volume of this cone?
First, divide the diameter in half to find the radius.
Now, use the formula to find the volume of the cone.
Example Question #11 : Volume Of A Three Dimensional Figure
A cone has a radius of inches and a height of inches. Find the volume of the cone.
The volume of a cone is given by the formula:
Now, plug in the values of the radius and height to find the volume of the given cone.
Certified Tutor