Question

Curved surface area of a given cylinder is 924 sq m.If ratio of radius and height of cylinder is 1:3.Then find the volume of cylinder

Answer 1

$\mathfrak{\huge{Answer:}}$

$\mathbb{GIVEN}$

Curved Surface Area of the cylinder = 924 sq. m

Ratio of the radius and the height of the cylinder = 1:3

$\mathbb{TO\:FIND}$

The Volume of the cylinder

$\mathbb{METHOD}$

Let the radius and the height be = x and 3x ( these assumptions have been made according to the ratios between the radius and the height, given in the question )

Curved Surface Area of the cylinder = $\sf{2 \pi r h}$

=》 $\sf{924 = 2 \pi r h}$

Solve this formed equation further

=》 $\sf{924 = 2 \pi \times 3x^{2}}$

=》 x = 7

x = 7 cm

3x = 21 cm

Volume of cylinder = $\sf{\pi r^{2} h}$

Volume = $\sf{\pi \times 7^{2} \times 21}$

Volume = $\sf{3234\:cm^{3}}$

The answer will be $\huge{\tt{3234\:cm^{3}}}$

Answer 2

Answer:

3234 cm³

Step By Step Explanation:

Given:

C.S.A of cylinder = 924 m²

Ratio of its radius and height = 1 : 3

Now,

Let radius be x cm and radius be 3x cm.

According To The Condition:

C.S.A = 924 m²

⇒ 2 π r h = 924 m²

⇒ 2 × 22/7 × x × 3 x = 924

⇒ 44/7 × 3x² = 924

⇒ 3x² = 924 × 7/44

⇒ 3x² = 21 × 7

⇒ x² = 7 × 7

⇒ x = 7

Therefore,

Radius = x = 7 cm

Height = 3x = 3 × 7 = 21 cm

Again,

Volume = π r² h

⇒ 22/7 × 7² × 21

⇒ 22 × 7 × 21

⇒ 3234 cm³

Hence, The required volume of cylinder is 3234 cm³.