Question

22. The curved surface area of a cylindrical tank of length 7m is 308 mſ. Find the area
of the base of the cylinder.​

Answer 1

Answer:

154

Step-by-step explan

Answer 2

$\underline{ \underline{ \Large \pmb{\sf { \purple{Answer:}} }} }$

✰ The area of the base of the cylinder is 154 m².

$\underline{ \underline{ \Large \pmb{\sf { \purple{Given:}} }} }$

• C.S.A of the cylinderical tank = 308 m²

• Length or height of the cylinderical tank = 7 m

$\underline{ \underline{ \Large \pmb{\sf { \purple{To \: calculate:}} }} }$

• Area of the base of the cylinder.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Calculation:}} }} }$

In order to find the base of the cylinderical tank, we need to find the base radius as the base of the cylinder is in the shape of a circle.We'll calculate the base radius by forming a linear equation with the help of the formula of the C.S.A of the cylinder.Then, we'll substitute the value of the radius in the formula of the area of the circular base.

⠀⠀⠀⠀⠀_____________

We know that,

⇒ Area of circle = πr² sq. units

Henceforth,

✰ Area of base of cylinder = πr²

We haven't been given the radius. Let's calculate it first. We know that,

${\underline {\boxed {\large {\bf \orange { {C.S.A}_{(Cylinder)} = 2 \pi r h } }}}}$

✰ r = base radius

✰ h = height

According to the question,

$\mapsto \rm { 308 = 2 \times \dfrac{22}{\cancel{7}} \times r \times \cancel{7} } \\ \\ \\ \mapsto \rm { 308 = 2 \times 22 \times r } \\ \\ \\ \mapsto \rm { 308 = 44 \times r } \\ \\ \\ \mapsto \rm { \dfrac{308 }{44} =r } \\ \\ \\ \mapsto \pmb{ \rm \red{ 7 \: m}}$

Henceforth,

• Base radius of the cylinderical tank is 7 m.

Now, we know that,

${\underline {\boxed {\large {\bf \orange { {Area}_{(Circle)} = \pi {r}^{2} } }}}}$

$\mapsto \rm { {Area}_{(Cylinder's \: base)} = \dfrac{22}{7} \times {7}^{2} } \\ \\ \\\mapsto \rm { {Area}_{(Cylinder's \: base)} = \dfrac{22}{\cancel{7}} \times 7 \times \cancel{7} } \\ \\ \\ \mapsto \rm { {Area}_{(Cylinder's \: base)} = 22 \times 7} \\ \\ \\ \mapsto\underline{\boxed{ \pmb{ \rm\red { {Area}_{(Cylinder's \: base)} = 154 \: {m}^{2} } }}}$

Therefore,

• The area of the base of the cylinder is 154 m².