# SSAT Upper Level Math : How to find the volume of a cone

## Example Questions

### Example Question #1 : Volume Of A Three Dimensional Figure

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)?      Explanation:

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 #2 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

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   Explanation:

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 #161 : 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 .      Explanation:

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 #11 : Volume Of A Three Dimensional Figure

A right cone has a volume of , a height of and a radius of the circular base of . Find .      Explanation:

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 #851 : Ssat Upper Level Quantitative (Math)

A cone has a diameter of and a height of . In cubic meters, what is the volume of this cone?     Explanation:

First, divide the diameter in half to find the radius.  Now, use the formula to find the volume of the cone.  ### Example Question #13 : Volume Of A Three Dimensional Figure

A cone has a radius of inches and a height of inches. Find the volume of the cone.     Explanation:

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. ### All SSAT Upper Level Math Resources 