SSAT Upper Level Math : Volume of a Three-Dimensional Figure

Example Questions

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Example Question #2 : Volume Of A Sphere

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Explanation:

The volume of a sphere, given its radius, is

Set , solve for , and double that to get the diameter.

The diameter is twice this, or 12.4 yards.

Example Question #1 : Volume Of A Three Dimensional Figure

The diameter of a sphere is . Give the volume of the sphere in terms of .

Explanation:

The diameter of a sphere is  so the radius of the sphere would be

The volume enclosed by a sphere is given by the formula:

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

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Explanation:

The volume enclosed by a sphere is given by the formula:

where  is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be meters. Now we can get:

Example Question #3 : How To Find The Volume Of A Sphere

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Explanation:

The volume of a sphere is:

Where is the radius of the sphere. We know the volume and can solve the formula for :

inches

So we can get:

Example Question #4 : How To Find The Volume Of A Sphere

A sphere has a diameter of  inches. What is the volume of this sphere?

Explanation:

To find the volume of a sphere, use the following formula:

, where  is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

Now, plug this value into the volume equation.

Example Question #5 : How To Find The Volume Of A Sphere

What is the volume of a sphere with a diameter of ?

Explanation:

Write the formula for the volume of the sphere.

The radius is half the diameter, which is five.  Substitute the value.

Example Question #2 : Volume Of A Three Dimensional Figure

What is the volume of a sphere with diameter 12 feet?

None of the other answers are correct

Explanation:

The radius of the sphere is half the diameter, or 6 feet; use the formula

.

Setting :

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)?

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 : 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

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 #3 : How To Find The Volume Of A Cone

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 .