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The adjoining figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 cm. The height of the cylinder and cone each is 4 cm. Find the volume of the solid.

The adjoining figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 cm. The height of the cylinder and cone each is 4 cm. Find the volume of the solid. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Mensuration

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Answer

Given, common radius, r = 7 cm

Height of cone, h = 4 cm

Height of cylinder, H = 4 cm

Volume of solid = Volume of cone + Volume of cylinder + Volume of hemisphere

=13πr2h+πr2H+23πr3=πr2(13h+H+23r)=227×72(13×4+4+23×7)=227×49(43+4+143)=22×7(4+12+143)=154×303=154×10=1540 cm3.= \dfrac{1}{3} π\text{r}^2\text{h} + π\text{r}^2\text{H} + \dfrac{2}{3} π\text{r}^3 \\[1em] = π\text{r}^2 \Big(\dfrac{1}{3} \text{h} + \text{H} + \dfrac{2}{3} \text{r}\Big) \\[1em] = \dfrac{22}{7} \times 7^2 \Big(\dfrac{1}{3} \times 4 + 4 + \dfrac{2}{3} \times 7 \Big) \\[1em] = \dfrac{22}{7} \times 49 \Big(\dfrac{4}{3} + 4 + \dfrac{14}{3} \Big) \\[1em] = 22 \times 7 \Big(\dfrac{4 + 12 + 14}{3} \Big) \\[1em] = 154 \times \dfrac{30}{3} \\[1em] = 154 \times 10 \\[1em] = 1540 \text{ cm}^3.

Hence, volume of solid is 1540 cm3.

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