# The diameter of the base of a cylinder is 21cm and its height is 18cm. A hemisphere and a cone of diameter same as that of the cylinder are joined on either side of the cylinder. If the height of the cone is 9cm, find the volume of solid obtained.

$\\\text{We have given: } \\ \text{Diameter of the base of a cylinder }=21 \text{ cm}\\ \text{Height of the cylinder } =18 \text{cm}$

\begin{aligned} &\text {Volume of the cylinder }=\pi r^{2} h\\ &V=\pi\left(\frac{21}{2}\right)^{2} \times 18\\ &V=6237 \mathrm{~cm}^{3} \end{aligned}

\\\text{Volume of the hemisphere with radius }=10.5 \text{cm} \\ \begin{aligned} \text {Volume } &=\frac{2}{3} \pi r^{3}=\frac{2}{3} \times\left(\frac{22}{7}\right) \times(10.5)^{3} \\ &=2425.5 \mathrm{~cm}^{3} \end{aligned}

\begin{aligned} &\text { Volume of the cone of height } 9 \mathrm{~cm} \text { and radius } 10.5 \mathrm{~cm}\\ &\text { Volume }=\frac{1}{3} \pi r^{2} h\\ &\text { Volume of the cone }=\frac{1}{3} \times\left(\frac{22}{7}\right) \times(10.5)^{2} \times 9=1039.5 \mathrm{~cm}^{3} \end{aligned}

$\\\\ \text{Now,}\\ \text{Volume of the solid obtained } = \text{Volume of the cylinder }+ \text{Volume of a cone }+ \text{Volume of the hemisphere} \\\\$

$\begin{array}{l} =6237+2425.5+1039.5 \\ =9702 \mathrm{~cm}^{3} \end{array}$

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