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

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例子Questions

例子Question #151 :Geometry

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:

$6.2 \;\textrm{yd}$

$12.4 \;\textrm{yd}$

$7.7 \;\textrm{yd}$

$9.3 \;\textrm{yd}$

$15.4 \;\textrm{yd}$

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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例子Question #1 :Volume Of A Three Dimensional Figure

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

Possible Answers:

$72\pi t^3$

$10\pi t^3$

$24\pi t^3$

$30\pi t^3$

$36\pi t^3$

Correct answer:

$36\pi t^3$

Explanation:

The diameter of a sphere is所以sp的半径here 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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例子Question #492 :Grade 8

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

Possible Answers:

1000m^3

1023.3m^3

723.3m^3

500m^3

523.6m^3

Correct answer:

523.6m^3

Explanation:

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

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

whereis 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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例子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:

$16.4\ inches$

$12.4\ inches$

$10.4\ inches$

$10\ inches$

$12\ inches$

Correct answer:

$12.4\ inches$

Explanation:

The volume of a sphere is:

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

Whereis 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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例子Question #4 :Volume Of A Three Dimensional Figure

一个球体的直径eter ofinches. What is the volume of this sphere?

Possible Answers:

104.7 in^3

458.3 in^3

523.6 in^3

632.9 in^3

Correct answer:

523.6 in^3

Explanation:

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

$\text{Volume}=\frac{4}{3}\pi\times r^3$ , whereis 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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例子Question #5 :Volume Of A Three Dimensional Figure

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

Possible Answers:

$200\pi$

$100\pi$

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

$150\pi$

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

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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例子Question #1 :Volume Of A Three Dimensional Figure

What is the volume of a sphere withdiameter12 feet?

Possible Answers:

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

$452.4\;ft^{3}$

None of the other answers are correct

$904.8 ft^{3}$

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

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

例子Questions

例子Question #151 :Geometry

例子Question #1 :Volume Of A Three Dimensional Figure

例子Question #492 :Grade 8

例子Question #3 :Volume Of A Three Dimensional Figure

例子Question #4 :Volume Of A Three Dimensional Figure

例子Question #5 :Volume Of A Three Dimensional Figure

例子Question #1 :Volume Of A Three Dimensional Figure

All SSAT Upper Level Math Resources

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