How to find the diameter of a sphere

Help Questions

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.

Return to subject

AI TutorYour personal study buddy

Question of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games