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Class 10 › Mathematics › Surface Areas and Volumes
CBSE2026Class Class 10 · Mathematics3 Marks · Short✅ Verified
A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use $\pi = \frac{22}{7}$)
✅ Answer & Solution
Radius $r = \frac{7}{2} = 3.5$ cm. Total height $= 20$ cm $=$ height of cylinder $+ 2r$ (two hemispherical ends). Height of cylinder $h = 20 - 2(3.5) = 20-7=13$ cm. Total Volume = Volume of cylinder + Volume of 2 hemispheres $= \pi r^2 h + 2\left(\frac{2}{3}\pi r^3\right) = \pi r^2\left(h+\frac{4r}{3}\right) = \frac{22}{7}\times \left(\frac{7}{2}\right)^2 \times \left(13+\frac{4\times 3.5}{3}\right) = \frac{22}{7}\times \frac{49}{4} \times \left(13+\frac{14}{3}\right) = \frac{22}{7}\times \frac{49}{4} \times \frac{53}{3} = \frac{22 \times 7 \times 53}{4 \times 3} = \frac{8162}{12} = 680.17$ cm³ (approx).
