Question

A three-dimensional figurehus a volume of 250 cubiccentimeters. Select the shapethat could match.1.TaFl. Asphere with a radus of 3.901cm2. Asphere with a diameter of 3.909073.А cone with a radius of 10.93 cmand a height of 2 cm.4. A cylinder with a radius of5.27cm and a neight of 4cm.S. A cylinder with a radius of1cm and a height of 8cm.

Answer 1

Volume is a measure of the amount of room in a three-dimensional space.

Generally represented mathematically as area x height.

1) A sphere has a volume measured mathematically as:

$V=\frac{4}{3}\pi\times r^3$$V=\frac{4}{3}\pi\times3.901^3=248.666\text{ cubic cm}$

2) Applying the same formulae, we have

$V=\frac{4}{3}\pi\times(\frac{3.90907}{2})^3=31.277\text{ cubic cm}$

3) For a cone, volume, V gives

$\begin{gathered} V=\frac{1}{3}\pi\times r^2h\text{ where h = perpendicular height} \\ V=\frac{1}{3}\pi\times10.93^2\times2=250.207\text{ cubic cm} \end{gathered}$

4) For a cylinder, V gives

$\begin{gathered} V=\pi r^2h\text{ } \\ V=\pi\times5.27^2\times4=349.005\text{ cubic cm} \end{gathered}$

5) For a cylinder, V gives

$V=\pi\times1^2\times8=25.133\text{ cubic cm}$

Therefore, sphere 1 and the cone will all give volumes of approximately 250 cubic cm