Question

In the given figure a metal container is in the form of a cylinder surmounted by a hemisphere. The internal height of the cylinder is 7m and the internal radius is 3.5m. Calculate (i) total area of the internal surface, excluding the base;(ii) the internal volume of the container in m3
pls answer quickly​

Answer 1

Given :-

• Cylinder is submounted by a hemisphere .

• Height of cylinder is 7 m .

• Radius of cylinder is 3.5 m.

To find :-

• Total surface area excluding base .

• Volume of container.

Solution :-

Formula used :-

${ \underline{ \underline{ \sf{ \implies \: LSA \: of \: cylinder = 2\pi.rh}}}}$

${ \underline{ \underline{ \sf{\implies \:LSA \: of \: hemisphere = 2\pi.{r}^{2}}}}}$

$\underline{ \underline{ \sf{ \implies \: volume \: of \: cyl. = \pi {r}^{2} h}}}$

${\underline{\underline{\sf{\implies \:Volume\:of\: Hemisphere= \frac{2}{3} \pi. {r}^{3}}}}}$

1. Surface area of given container .

→ LSA of cylinder + CSA of hemisphere .

→ LSA of cylinder = 2 $\frac{22}{7}$ ×3.5×7

$\sf{\implies 2 \times 22 \times 3.5}$

${ \underline{ \underline{ \sf{ \implies \: 154 \: {m}^{2} = LSA}}}}$

→ CSA of hemisphere = 2 $\frac{22}{7} \times {3.5}^{2}$

$\sf{ \implies \: 154 \times \frac{3.5}{7} }$

$\sf{ \implies 22 \times 3.5}$

${ \underline{ \underline {\sf{ \implies \: 77 \: {m}^{2} = \: CSA}}}}$

Internal surface area of container = 154 + 77

${\boxed{\boxed{\sf{ \implies 271 \: is \: the \: required\: area }}}}$

2. Volume of container

→ Volume of cylinder + Volume of hemisphere.

→ Volume of cylinder = $\sf{\frac{22}{7} \times {3.5}^{2} \times 7 }$

$\sf{\implies 22 \times 3.5 \times 3.5 }$

${ \underline{ \underline{ \sf{ \implies \: 269.5 \: {m}^{3} = \: volume}}}}$

→ Volume of hemisphere = $\sf{\frac{2}{3} \times \frac{22}{7} {3.5}^{3} }$

$\sf{\implies \: \frac{2}{3} \times 22 \times 0.5 \times 3.5 \times 3.5}$

${\underline{\underline{\sf{\implies 89.84 {m}^{3} \: = \: volume}}}}$

Volume of container = 269.5 + 89.84

${ \boxed{ \boxed{ \sf{ \implies \: 359.34 \: {m}^{3} }}}}$