Question

the base of area of right circular cylinder is 154 cm square and volume of cylinder is 6160 cm^3 the curved surface area of cylinder will be​

Answer 1

Given,

Volume of cylinder, V = 6160 cm³

Base of area of right circular cylinder= 154 cm²

To find,

Curved surface area of the cylinder (CSA)

Solution,

As, it is given,

Base of area of right circular cylinder= 154 cm²

∴πr²= 154 -- (1)

⇒r²=$\frac{154}{\pi }$

On substituting π = $\frac{22}{7}$, we get

⇒r²=$\frac{154}{\frac{22}{7} }$

⇒r²=$\frac{(154)(7)}{22}$

⇒r²=49

∴r=7 cm

Now, Volume of cylinder, V = 6160 cm³

∴πr²h = 6160 --(2)

Dividing the equation 2 by 1,we get

$\frac{\pi r^{2}h}{\pi r^{2}}$= $\frac{6160}{154}$

⇒h=$\frac{6160}{154}$

⇒h=40 cm

Now, Using the formula for Curved surface area of the cylinder (CSA)

∴CSA=2πrh

⇒CSA=2×$\frac{22}{7}$×7×40

⇒CSA= 1760

Hence, Curved surface area of the cylinder (CSA) is 1760 cm²

Answer 2

Given:

The base of area of right circular cylinder is 154 cm²

Volume of cylinder is 6160 cm³

To find :

The curved surface area of cylinder

Formula to be used:

Base area of right circular cylinder = πr²

Volume of right circular cylinder = πr²h

Curved surface area of right circular cylinder = 2πrh

Solution:

Step 1 of 2:

The base of area of right circular cylinder is 154 cm²

Base area of right circular cylinder = πr²

πr² =  154 cm²

Then, the radius of the cylinder is,

$\frac{22}{7}$ × r² = 154

r² = 154 × $\frac{7}{22}$

r² = 7 × 7

r² = 7²

radius = 7 cm

Volume of right circular cylinder = πr²h

πr²h = 6160 cm³

Then, the height of the cylinder is,

154(h) = 6160

h = $\frac{6160}{154}$

height = 40 cm

Step 2 of 2:

Curved surface area of right circular cylinder = 2πrh

Curved surface area of right circular cylinder = 2 × $\frac{22}{7}$ × 7 × 40

Curved surface area of right circular cylinder = 2 × 22 × 40

Curved surface area of right circular cylinder = 1760 cm²

Final answer:

The curved surface area of cylinder is 1760 cm²