### All SSAT Upper Level Math Resources

## 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)?

**Possible Answers:**

**Correct answer:**

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 : Volume Of A Three Dimensional Figure

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:**

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**Correct answer:**

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 : Volume Of A Three Dimensional Figure

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:**

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

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

**Possible Answers:**

**Correct answer:**

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 #2 : 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:**

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.

**Possible Answers:**

**Correct answer:**

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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