Question

Select all the correct figures.Select the figures with a volume greater than 400 cubic centimeters.

Answer 1

Volume of figure 1

The figure is a Cuboid

The formula for the volume of a cuboid is,

$V=lwh$

Given:

$l=14cm,w=5cm,h=6cm$

Therefore,

$\begin{gathered} V=14\times5\times6=420 \\ \therefore V=420cm^3 \end{gathered}$

Volume of figure 2

The figure is a Cylinder.

The formula for the volume of a cylinder is,

$V=\pi r^2h$

Given:

$r=3,h=14$

Therefore,

$\begin{gathered} V=\frac{22}{7}\times3\times3\times14=22\times3\times3\times2=396 \\ \therefore V=396cm^3 \end{gathered}$

Volume of figure 3

The figure is a Cone

The formula for the volume of a cone is,

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

Given:

$r=5,h=15$

Therefore,

$\begin{gathered} V=\frac{1}{3}\times\pi\times5^2\times15=392.69908 \\ \therefore V=392.69908cm^3 \end{gathered}$

Volume of figure 4

The figure is a Sphere

The formula for the volume of a sphere is,

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

Given:

$r=5$

Therefore,

$\begin{gathered} V=\frac{4}{3}\times\pi\times5^3=523.59878 \\ \therefore V=523.59878cm^3 \end{gathered}$

Volume of figure 5

The figure is a Rectangle-based pyramid

The formula for the volume of a rectangle-based pyramid is,

$V=\frac{1}{3}lwh$

Given:

$l=10cm,w=9cm,h=12$

Therefore,

$\begin{gathered} V=\frac{1}{3}\times10\times9\times12=360 \\ \therefore V=360cm^3 \end{gathered}$

Hence, the figures with a volume greater than 400 cubic centimeters are

$\begin{gathered} Figure\text{1\lparen Cuboid\rparen with the volume of 420cm}^3 \\ Figure4\text{ \lparen Sphere\rparen with the volume of 523.59878}cm^3 \end{gathered}$