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

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Example Questions

Example Question #1 : How To Find The 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)?

Possible Answers:

$6.2 \;\textrm{yd}$

$12.4 \;\textrm{yd}$

$15.4 \;\textrm{yd}$

$9.3 \;\textrm{yd}$

$7.7 \;\textrm{yd}$

Correct answer:

$12.4 \;\textrm{yd}$

Explanation:

The volume of a sphere, given its radius, is

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

Set V = 1,000 , solve for , and double that to get the diameter.

$1,000= \frac{4\pi r^{3}}{3}$

$r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

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

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

Possible Answers:

$10\pi t^3$

$36\pi t^3$

$72\pi t^3$

$30\pi t^3$

$24\pi t^3$

Correct answer:

$36\pi t^3$

Explanation:

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

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

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3t)^3=\frac{4}{3}\pi\times 27t^3\Rightarrow Volume=36\pi t^3$

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Example Question #1332 : Concepts

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

Possible Answers:

1000m^3

523.6m^3

1023.3m^3

723.3m^3

500m^3

Correct answer:

523.6m^3

Explanation:

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

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

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times 5^3=\frac{4}{3}\times \pi \times 125\approx 523.6 m^3$

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Example Question #3 : Volume Of A Three Dimensional Figure

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

Possible Answers:

$12.4\ inches$

$10.4\ inches$

$16.4\ inches$

$12\ inches$

$10\ inches$

Correct answer:

$12.4\ inches$

Explanation:

The volume of a sphere is:

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

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

$Volume=\frac{4}{3}\pi r^3=1000\Rightarrow r^3=\frac{3\times1000 }{4\pi}\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$Diameter=2r=2\times 6.2=12.4inches$

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

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

Possible Answers:

523.6 in^3

458.3 in^3

632.9 in^3

104.7 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 #3 : Volume Of A Three Dimensional Figure

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

Possible Answers:

$\frac{500}{3}\pi$

$150\pi$

$100\pi$

$\frac{100}{3}\pi$

$200\pi$

Correct answer:

$\frac{500}{3}\pi$

Explanation:

Write the formula for the volume of the sphere.

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

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

$V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3=\frac{4}{3}\pi (125)= \frac{500}{3}\pi$

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Example Question #3 : Volume Of A Three Dimensional Figure

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

Possible Answers:

$7,238.2\;ft^{3}$

None of the other answers are correct

$904.8 ft^{3}$

$452.4\;ft^{3}$

$3,619.1\;ft^{2}$

Correct answer:

$904.8 ft^{3}$

Explanation:

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

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

Setting r=6 :

$V= \frac{4}{3} \pi \cdot 6^{3} \approx904.8 ft^{3}$

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

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

All SSAT Upper Level Math Resources

Example Questions

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

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

Example Question #1332 : Concepts

Example Question #3 : Volume Of A Three Dimensional Figure

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

Example Question #3 : Volume Of A Three Dimensional Figure

Example Question #3 : Volume Of A Three Dimensional Figure

All SSAT Upper Level Math Resources

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