Question

The volume of a cone is 113.04 mm2. What is the approximate volume of a sphere that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth.

Answer 1

Answer:

$V=169.56\ mm^3$

Step-by-step explanation:

we know that

The volume of the cone is given by te formula

$V=\frac{1}{3}\pi r^{2}h$

we have

$V=113.04\ mm^3$

substitute

$113.04=\frac{1}{3}\pi r^{2}h$

$339.12=\pi r^{2}h$ ----> equation A

Remember that

A sphere has the same height and a circular base with the same diameter

That means----> The diameter of the sphere is equal to the height of the cone and the radius of the sphere is equal to the radius of the base of cone

$r=\frac{h}{2}$

equation A is equal to

$339.12=\pi (\frac{h}{2})^{2}h$

$339.12=\pi (\frac{h^3}{3})$

$1,017.36=\pi h^3$ -----> equation B

The volume of the sphere is given by

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

substitute

$V=\frac{4}{3}\pi (\frac{h}{2})^{3}$

$V=\frac{4}{24}\pi h^3$

$V=\frac{1}{6}\pi h^3$

substitute equation B in the expression above

$V=\frac{1}{6}(1,017.36)=169.56\ mm^3$