How to find the radius of a sphere Flashcards - ISEE Upper Level (grades 9-12) Quantitative Reasoning

The volume of a sphere with radius is

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

To find the radius in yards, we set and solve for .

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

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

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

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

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

$r = \sqrt[3]{ \frac{3}{4\pi} } = \sqrt[3]{ \frac{3\cdot 2 \pi^{2}}{4\pi \cdot 2 \pi^{2}} }= \sqrt[3]{ \frac{6 \pi^{2}}{8 \pi^{3}} } = \frac{ \sqrt[3]{6 \pi^{2}} } {2\pi}$ yards.

Since the problem requests the radius in inches, multiply by 36:

$36 \times \frac{ \sqrt[3]{6 \pi^{2}} } {2\pi} = \frac{ 18\sqrt[3]{6 \pi^{2}} } {\pi}$

How to find the radius of a sphere - ISEE Upper Level (grades 9-12) Quantitative Reasoning

The volume of a sphere is one cubic yard. Give its radius in inches.

How to find the radius of a sphere - ISEE Upper Level (grades 9-12) Quantitative Reasoning

The volume of a sphere is one cubic yard. Give its radius in inches.

The volume of a sphere with radius is . To find the radius in yards, we set and solve for . yards. Since the problem requests the radius in inches, multiply by 36: