How to find the diameter of a sphere

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SAT Math › How to find the diameter of a sphere

Questions 1 - 3

1

Find the diameter of a sphere with a surface area of $20\pi$ .

$2\sqrt5$

$\sqrt5$

$\sqrt{10}$

$2\sqrt{10}$

Explanation

Write the formula to find the surface area of a sphere.

$A=4\pi r^2$

Substitute the area and solve for the radius.

$20\pi=4\pi r^2$

$r=\sqrt5$

The diameter is double the radius.

$d=2\sqrt5$

2

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

$2\sqrt[3]{\frac{9}{\pi}}$

$2\sqrt[3]{\frac{18}{\pi}}$

$\sqrt[3]{\frac{18}{\pi}}$

$\frac{3}{\pi ^3}$

$\sqrt[3]{\frac{9}{\pi}}$

Explanation

Write the formula for the volume of a sphere.

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

Substitute the volume.

$12=\frac{4}{3}\pi r^3$

Multiply by $\frac{3}{4\pi}$ on both sides in order to isolate the term.

$12\cdot \frac{3}{4\pi}=\frac{4}{3}\pi r^3\cdot \frac{3}{4\pi}$

$\frac{9}{\pi}= r^3$

Cube root both sides.

$\sqrt[3]{\frac{9}{\pi}}= r$

The diameter is double the radius.

$d= 2\sqrt[3]{\frac{9}{\pi}}$

The answer is: $2\sqrt[3]{\frac{9}{\pi}}$

3

What is the diameter of a sphere if the surface area is $64\pi$ ?

$4\sqrt3$

$8\sqrt3$

Explanation

Write the formula for the surface area of a sphere.

$A=4\pi r^2$

Substitute the area and find the radius.

$64\pi=4\pi r^2$

The diameter is double the radius.

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