# If the lateral surface a cylinder is 94.2 cm 2 and its height is 5 cm, then find

I. Radius of its base and

II. Its volume

Answer

Verified

327.3k+ views

Hint: Compute radius from lateral surface area, proceed to find volume using the same radius.

Complete step-by-step answer:

Given, h= 5 cm

Let the radius be r cm, Now

(i) We know, Lateral/Curved Surface area=$2\pi rh$

Substituting all the values , we have

$

\Rightarrow 94.2c{m^2} = 2\pi rh \\

\Rightarrow 94.2c{m^2} = 2 \times 3.14 \times r \times 5cm \\

\Rightarrow r = 3cm \\

$

(ii) We know, Volume of cylinder= $\pi {r^2}h$

Substituting all the values along with value of r we found , we will have

$

\Rightarrow \pi {r^2}h = 3.14 \times 3 \times 3 \times 5 \\

= 141.2c{m^3} \\

$

Note: Formula of curved and total surface area, volume of general figures must be known for such

similar problems.

Complete step-by-step answer:

Given, h= 5 cm

Let the radius be r cm, Now

(i) We know, Lateral/Curved Surface area=$2\pi rh$

Substituting all the values , we have

$

\Rightarrow 94.2c{m^2} = 2\pi rh \\

\Rightarrow 94.2c{m^2} = 2 \times 3.14 \times r \times 5cm \\

\Rightarrow r = 3cm \\

$

(ii) We know, Volume of cylinder= $\pi {r^2}h$

Substituting all the values along with value of r we found , we will have

$

\Rightarrow \pi {r^2}h = 3.14 \times 3 \times 3 \times 5 \\

= 141.2c{m^3} \\

$

Note: Formula of curved and total surface area, volume of general figures must be known for such

similar problems.

Last updated date: 04th Jun 2023

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Total views: 327.3k

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