Math Problem Solver

The radius of a sphere is $\frac{\sqrt[3]{3150}}{\sqrt[3]{\pi}} \approx 10.01\, \text{mm}$.

Note: Approximate solutions are rounded to the nearest hundredths place.

Given: $$\begin{aligned}V&=4200\end{aligned}$$

Radius

The radius of a sphere is given by the equation: $$\begin{aligned}V&=\frac{4}{3} \pi r^{3}\end{aligned}$$ where $V$ is volume and $r$ is radius.

Solution:$$\begin{aligned}V&=\frac{4}{3} \pi r^{3}\\4200&=\frac{4}{3} \pi r^{3}\\r&=\frac{\sqrt[3]{3150}}{\sqrt[3]{\pi}}\end{aligned}$$

A sphere is a three dimensional solid that has no flat surfaces, corners, or edges. Its radius r is the distance between the center of the sphere and any point on the surface of the sphere. Its diameter d is twice the radius, forming a line segment passing through the center of the sphere.

The circumference C of a sphere is the distance around the cross section containing the center of a sphere, i.e. the largest circular cross section of a sphere. $$\begin{aligned} C &= 2 \pi r \\ &= \pi d \end{aligned}$$

The surface area S of a sphere is the region occupied by its surface. $$S = 4 \pi r^{2}$$

The volume V of a sphere is the amount of space it occupies. $$V = \frac{4}{3} \pi r^{3}$$