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

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #1 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

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)?

Possible Answers:

Correct answer:

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 #1 : 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)?

Possible Answers:

6333

Correct answer:

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

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 .

Possible Answers:

Correct answer:

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 #1 : How To Find The Volume Of A Cone

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

Possible Answers:

Correct answer:

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

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

Possible Answers:

Correct answer:

Explanation:

First, divide the diameter in half to find the radius.

Now, use the formula to find the volume of the cone.

Example Question #2 : How To Find The Volume Of A Cone

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

Possible Answers:

Correct answer:

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.

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