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HSPT Math : Geometry

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Example Questions

Example Question #1 : Solid Geometry

What is the volume of a right cone with a diameter of 6 cm and a height of 5 cm?

Possible Answers:

$60\pi \ cm^{3}$

$15\pi \ cm^{3}$

$120\pi \ cm^{3}$

$45\pi \ cm^{3}$

$180\pi \ cm^{3}$

Correct answer:

$15\pi \ cm^{3}$

Explanation:

The general formula is given by $V = 1/3Bh = 1/3\pi r^{2}h$ , where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

$V=\frac{\pi 3^2\times 5}{3}=15\pi$

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

There is a large cone with a radius of 4 meters and height of 18 meters. You can fill the cone with water at a rate of 3 cubic meters every 25 seconds. How long will it take you to fill the cone?

Possible Answers:

$41\ \textup{minutes}\ 53\ \textup{seconds}$

$800\ \textup{minutes}$

$600\ \textup{minutes}$

$60\ \textup{minutes}$

$3\ \textup{minutes}\ 20\ \textup{seconds}$

Correct answer:

$41\ \textup{minutes}\ 53\ \textup{seconds}$

Explanation:

First we will calculate the volume of the cone

$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi\cdot 4^{2}\cdot 18=96\pi\ m^{3}$

Next we will determine the time it will take to fill that volume

$96\pi \ m^{3}\times \frac{25\ s}{3\ m^{3}}=800\pi \ s$

We will then convert that into minutes

$800\pi \ s\times \frac{1\ minute}{60\ seconds}=13.\overline{3}\pi \ minutes\approx 41.9\ minutes\approx 41\ minutes\ 53\ seconds$

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Example Question #3 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

The height of a cylinder is two times the length of the radius of the circular end of a cylinder. If the volume of the cylinder is $16\pi$ , what is the height of the cylinder?

Possible Answers:

$2\sqrt{2}$

Correct answer:

Explanation:

The volume of a cylinder is:

$Volume=\pi r^2h$

where is the radius of the circular end of the cylinder and is the height of the cylinder.

Since h=2r , we can substitute that into the volume formula. So we can write:

$Volume=\pi r^2h$

$16\pi=\pi r^2\cdot (2r)$

$16\pi =2\pi r^{3}$

$16=2r^{3}$

$8=r^{3}$

r=2

So we get:

$h=2r=2\times 2=4$

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Example Question #1 : How To Find The Volume Of A Cylinder

A cylinder has a diameter of inches and a height of inches. Find the volume, in cubic inches, of this cylinder.

Possible Answers:

100.5 in^3

402.1 in^3

98.3 in^3

308.9 in^3

Correct answer:

100.5 in^3

Explanation:

$\text{Volume of cylinder}=\pi \times \text{radius}^2 \times \text{height}$

Since we are given the diameter, divide that value in half to find the radius.

$\text{radius}=8\div2=4$

Now plug this value into the equation for the volume of a cylinder.

$\text{Volume}=\pi \times 4^4 \times 2$

$\text{Volume}=\pi \times 32=100.5$ in^3

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Example Question #212 : Geometry

Find the volume, in cubic inches, of a cylinder that has a radius of inches and a height of inches.

Possible Answers:

737.5 in^3

3308.1 in^3

4456.1 in^3

2695.3 in^3

Correct answer:

3308.1 in^3

Explanation:

The formula to find the volume of a cylinder is $\pi r^2\times height$ .

Now, plug in the given numbers into this equation.

$\text{Volume}=\pi \times 9^2 \times 13$

$\text{Volume}=\pi \times 1053=3308.1$ in^3

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Example Question #2 : Volume Of A Three Dimensional Figure

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

Possible Answers:

104.7 in^3

523.6 in^3

458.3 in^3

632.9 in^3

Correct answer:

523.6 in^3

Explanation:

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

$\text{Volume}=\frac{4}{3}\pi\times r^3$ , 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.

$r=10\div2=5$

Now, plug this value into the volume equation.

$\text{Volume}=\frac{4}{3}\pi\times 5^3$

$\text{Volume}=\frac{4}{3}\pi\times 125$

$\text{Volume}=\frac{500}{3}\pi=523.6$ in^3

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Example Question #1991 : Hspt Mathematics

$\textup{What is the volume of a sphere with a diameter of 14?}$

Possible Answers:

$\frac{49}{3}\pi$

$49\pi$

$\frac{1372}{3} \pi$

$\frac{10976}{3} \pi$

$196\pi$

Correct answer:

$\frac{1372}{3} \pi$

Explanation:

Write the formula for the volume of a sphere.

$V=\frac{4}{3}\pi r^3$

Since the diameter is 14 the radius is half the diameter, which is 7. Substitute the radius and solve for the volume.

$V=\frac{4}{3}\pi (7)^3= \frac{1372}{3} \pi$

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Example Question #211 : Geometry

Find the area of a cylinder with radius 7 and height 2.

Possible Answers:

$14\pi$

$49\pi$

$98\pi$

$28\pi$

Correct answer:

$98\pi$

Explanation:

To solve, simply use the formula for the volume of a cylinder.

Thus,

$V=\pi{r^2}h$

Given the height is 2 and the radius is 7, substitute these values into the above formula to solve for volume.

$\\V=\pi*7^2*2\\V=\pi*49*2\\V=98\pi$

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Example Question #1993 : Hspt Mathematics

Cylinder

Which expression is equal to 40% of the volume of the above cylinder?

Possible Answers:

$30,000 \pi$

$2,500 \pi$

$4,800 \pi$

$400 \pi$

Correct answer:

$4,800 \pi$

Explanation:

The volume of the cylinder can be calculated by setting r = 20 and h = 30 in the formula

$V = \pi r^{2}h$

$V = \pi \cdot 20 ^{2} \cdot 30$

$V = \pi \cdot 400 \cdot 30$

$V =12,000 \pi$

40% of this volume is

$12,000 \pi \cdot \frac{40}{100} = 4,800 \pi$

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Example Question #1994 : Hspt Mathematics

Cylinder

The volume of the above cylinder is 80% of what number?

Possible Answers:

$45,000 \pi$

$28,000 \pi$

$2,625 \pi$

$1,680 \pi$

Correct answer:

$45,000 \pi$

Explanation:

The volume of the cylinder can be calculated by setting r = 30 and h = 40 in the formula

$V = \pi r^{2}h$

$V = \pi \cdot 30 ^{2} \cdot 40$

$V = \pi \cdot 900 \cdot 40$

$V =36,000 \pi$

This is 80% of the number

$36,000 \pi \div \frac{80}{100} = 36,000 \pi \cdot \frac{100} {80}= 45,000 \pi$

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : Solid Geometry

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

Example Question #3 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

Example Question #1 : How To Find The Volume Of A Cylinder

Example Question #212 : Geometry

Example Question #2 : Volume Of A Three Dimensional Figure

Example Question #1991 : Hspt Mathematics

Example Question #211 : Geometry

Example Question #1993 : Hspt Mathematics

Example Question #1994 : Hspt Mathematics

All HSPT Math Resources

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