Question
From a solid cylinder whose height is 2.4 cm and the diameter 1.4 cm, a cone of the same height and same diameter is carved out. Find the volume of the remaining solid to the nearest cm$^3$.
✓
Answer
Radius of a cylinder = Radius of a cone (r) = 0.7 cm
Height of a cylinder = Height of a cone (h) = 2.4 cm
Volume of the remaining solid = Volume of the cylinder – Volume of a cone
$
\begin{aligned}
& =\pi r ^2 h -\frac{1}{3} \pi r ^2 h cm ^3 \\
& =\pi r ^2 h \left(1-\frac{1}{3}\right) cm ^3 \\
& =\frac{22}{7} \times 0.7 \times 0.7 \times 2.4 \times \frac{2}{3} cm ^3 \\
& =\frac{22}{7} \times \frac{7}{10} \times \frac{7}{10} \times \frac{24}{10} \times \frac{2}{3} cm ^3 \\
& =\frac{22 \times 7 \times 24 \times 2}{1000 \times 3} cm ^3 \\
& =\frac{22 \times 7 \times 8 \times 2}{1000} cm ^3 \\
& =2.464 cm ^3 \\
& =2.46 cm ^3
\end{aligned}
$
Volume of the remaining soild $=2.46 cm ^3$
Height of a cylinder = Height of a cone (h) = 2.4 cm
Volume of the remaining solid = Volume of the cylinder – Volume of a cone
$
\begin{aligned}
& =\pi r ^2 h -\frac{1}{3} \pi r ^2 h cm ^3 \\
& =\pi r ^2 h \left(1-\frac{1}{3}\right) cm ^3 \\
& =\frac{22}{7} \times 0.7 \times 0.7 \times 2.4 \times \frac{2}{3} cm ^3 \\
& =\frac{22}{7} \times \frac{7}{10} \times \frac{7}{10} \times \frac{24}{10} \times \frac{2}{3} cm ^3 \\
& =\frac{22 \times 7 \times 24 \times 2}{1000 \times 3} cm ^3 \\
& =\frac{22 \times 7 \times 8 \times 2}{1000} cm ^3 \\
& =2.464 cm ^3 \\
& =2.46 cm ^3
\end{aligned}
$
Volume of the remaining soild $=2.46 cm ^3$
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