Question

What is the approximate diameter of a sphere with a volume of 34 cm^3 ?A. 2cmB. 6cmC.5cmD.4cm

Answer 1

D. 4 cm

Step-by-step explanation

The volume of the sphere is given as 34 cm^3

The volume of a sphere can be calculated using:

`V\text{ = }(4)/(3)\pi\cdot r^3`

We need to find the radius first. We have:

`\begin{gathered} 34\text{ = }(4)/(3)\cdot\pi\cdot r^3 \\ \text{Collect like terms:} \\ \frac{34\cdot\text{ 3}}{4\cdot\text{ }\pi}=r^3 \\ \Rightarrow r^3\text{ = 8.12} \\ r\text{ = }\sqrt[3]{8.12} \\ r\text{ = 2.009 cm} \end{gathered}`

The diameter is twice is the value of the radius, so:

D = 2 * r

D = 2 * 2.009

D = 4.018 cm

Approximately, the diameter is 4 cm.