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Mensuration — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSMensuration5 Marks
Question
Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.
✓

Answer

Radius of the cone = Radius of the cylinder

$
r =\frac{3}{2} cm
$

Height of the cone $( H )=2 cm$
Height of the cylinder $(h)=12-(2+2) cm =8 cm$
Volume of the model $=$ Volume of the cylinder + Volume of 2 cones
$
\begin{aligned}
& =\pi r ^2 h +2 \times \frac{1}{3} \pi r ^2 H \\
& =\pi r ^2\left( h +\frac{2}{3} H \right) cm ^3 \\
& =\frac{22}{7} \times \frac{3}{2} \times \frac{3}{2}\left(8+\frac{2}{3} \times 2\right) cm ^3 \\
& =\frac{11 \times 3 \times 3}{7 \times 2}\left(\frac{24+4}{3}\right) cm ^3 \\
& =\frac{11 \times 3 \times 3 \times 28}{7 \times 2 \times 3} cm ^3 \\
& =\frac{11 \times 3 \times 4}{2} cm ^3
\end{aligned}
$
= 11 × 3 × 2 cm$^3$
= 66 cm$^3$
Volume of the model = 66 cm$^3$

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