Question

If the volume of a sphere is 36 cubic units, what is the radius? 3 units 4√3 units 9 units

Answer 1

Answer:

radius = 2.05 units

Step-by-step explanation:

The volume of a sphere is given by the formula: $V=\frac{4}{3} \pi r^3$. In this formula:

• V = volume of the sphere
• r = radius of the sphere

Since we are given the volume of the sphere (36 units^3), we just need to solve for r in the equation for the volume of a sphere.

Substitute 36 for V into the formula and solve for r.

$36=\frac{4}{3} \pi r^3$

Divide both sides by $\frac{4}{3}$. To do this, multiply 36 by the reciprocal of $\frac{4}{3}$.

• $36\times \frac{3}{4}$
• $36\times \frac{3}{4} =\frac{108}{4} \rightarrow 27$

Simplify and rewrite the equation.

$27=\pi r^3$

Now divide both sides of the equation by pi ($\pi$).

• $27\div\pi=8.59436692696$

Rewrite the equation.

$8.59436692696=r^3$

To isolate and solve for r, cube root both sides of the equation.

• $r=\sqrt[3]{8.59436692696}$
• $r=2.04835218977$

The radius of this sphere is 2.04835218977 units. If your question wants this rounded to the nearest:

• whole number: 2 units
• tenth: 2.0 units
• hundredth: 2.05 units
• thousandth: 2.048 units

I'll just give the answer rounded to the nearest hundredth as that seems the most popular.

Answer 2

Well the unit would be 2 as a whole number but rounded it would be 2.05.
So the answer might as well be 2.05