Question

14. Find the volume of a cylinder with the following dimensions,
(1) Radius of the base = 14 cm and height = 36 cm
(11) Radius of the base = 21 cm and height = 1.5 m
(111) Diameter of the base = 7 m and height =5 m
(iv) Area of the base = 324 cm? and height = 8 cm
3
plz tell me the full explanation of question 3 and 4 ​

Answer 1

To Find :-

• The volume of cylinder

Solution :-

Formula used :-

$\dag \: \underline{ \boxed{ \bf{ \red{Volume \: of \: cylinder = \pi \: {r}^{2}h}}}}$

1. Radius of the base = 14 cm and height = 36 cm

Answer :-

$\bf{Volume \: of \: cylinder= \: \pi {r}^{2}h} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times {(14)}^{2} \times 36} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times 14 \times 14 \times 36} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{ \cancel{7}} \times \cancel{14} \times 14 \times 36} \\ \\ \\ \sf{\longrightarrow \: 22 \times 2 \: \times 14 \times 36} \\ \\ \\ \bf{ \longrightarrow \: 22176 {cm}^{3}} \: \: \: \: \: \: \bigstar$

2. Radius of the base = 21cm and height = 1.5m [ 150cm = 1.5m ]

Answer :-

$\bf{Volume \: of \: cylinder= \: \pi {r}^{2}h} \: \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times {(21)}^{2} \times 150} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times 21 \times 21 \times 150} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{ \cancel{7}} \times \cancel{21} \times 21 \times 150} \\ \\ \\ \sf{\longrightarrow \: 22 \times 3 \: \times 21 \times 150} \\ \\ \\ \bf{ \longrightarrow \: 207900 {cm}^{3}} \: \: \: \: \: \: \bigstar$

3. Diameter of the base = 7m and height = 5m

Answer :-

First we need to find out the radius,

$\dag \: \: \underline{\boxed{ \red{\sf{radius = \dfrac{diameter}{2}}}}}$

$\sf{ \longrightarrow \: \dfrac{7}{2}} \\ \\ \bf{\longrightarrow \: 3.5m}$

Radius = 3.5m.

$\bf{Volume \: of \: cylinder= \: \pi {r}^{2}h} \: \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times {(3.5)}^{2} \times 5} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times 3.5 \times 3.5 \: \times 5} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{ \cancel{7}} \times \cancel{3.5} \times 3.5 \times 5} \\ \\ \\ \sf{\longrightarrow \: 22 \times 0.5 \: \times 3.5 \times 5} \\ \\ \\ \bf{ \longrightarrow \: 192.5 {m}^{3}} \: \: \: \: \: \: \bigstar$

4. Area of the base = 324cm and height = 8cm

Answer :-

First we need to find out the radius,

$\bf{Area \: of \: the \: base = \pi {r}^{2}} \\ \\ \\ \sf{ \longrightarrow \: \dfrac{22}{7} \times \: {r}^{2} = 324} \\ \\ \\ \sf{ \longrightarrow \: {r}^{2} = \dfrac{324 \times 7}{22}} \\ \\ \\ \sf{ \longrightarrow \: {r}^{2} = \dfrac{2268}{22}}$

Now, Volume of cylinder

$\bf{Volume \: of \: cylinder= \: \pi {r}^{2}h} \: \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times {\bigg( \frac{2268}{22}\bigg)^{2} } \times 8} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{7} \times \: \dfrac{2268}{22} \times \: \dfrac{2268}{22} \times 8} \\ \\ \\ \sf{\longrightarrow \: \dfrac{22}{ \cancel{7}} \times {\dfrac{ \cancel{2268}}{22}} \times \dfrac{2268}{22} \times 8} \\ \\ \\ \sf{\longrightarrow \: \cancel{22} \times \dfrac{324}{ \cancel{22}} \: \times \: \dfrac{2268}{22} \times 8} \\ \\ \\ \sf{\longrightarrow \: 324\: \times \: \dfrac{2268}{ \cancel{22}} \times \cancel{8}} \\ \\ \\ \sf{\longrightarrow \: 324 \: \times \: \dfrac{2268}{11} \times 4} \\ \\ \\ \sf{ \longrightarrow \: \dfrac{2939328}{11}} \\ \\ \\ \bf{ \longrightarrow \: 267211.63 {cm}^{3}} \: \: \: \: \: \bigstar$