Question

Match the following solid objects with the expressions of their volume.

• A. $2{{\mathrm{\pi r}}_1}^2{h}_1+{{\mathrm{\pi r}}_2}^2{h}_2$
• B. ${\mathrm{\pi r}}^{2}h+\frac{2}{3}{\mathrm{\pi r}}^3$
• C. ${\mathrm{\pi r}}^{2}h-\frac{1}{3}{\mathrm{\pi r}}^{2}h$

Answer 1

Volume of this solid object
= Volume of the cylinder - volume of the cone
= $\pi r^{2}h-\frac{1}{3}\pi r^{2}h$
$\therefore$ Volume of this solid object
= $\pi r^{2}h-\frac{1}{3}\pi r^{2}h$


Volume of this solid object
= Volume of the cylinder + Volume of hemisphere
= $\pi r^{2}h+\frac{2}{3}\pi r^3$
$\therefore$ Volume of this solid object
= $\pi r^{2}h+\frac{2}{3}\pi r^3$


Volume of this solid object
= Volume of two cylinders with radii $r_1$ + Volume of cylinder with radius $r_2$
= $2\times \pi {r_1}^2{h}_1+\pi {r_2}^2{h}_2$
= $2\pi {r_1}^2{h}_1+\pi {r_2}^2{h}_2$
$\therefore$ ​Volume of this solid object
= $2\pi {r_1}^2{h}_1+\pi {r_2}^2{h}_2$