The volume of a right circular cylinder is 4851 cm³ and its curved surface area is 462 cm². If this cylinder is generated by rotating a rectangle about its length by 360°, what will be the perimeter (in cm) of this rectangle?
Use $$\pi$$ = $$\frac{22}{7}$$​

Correct option is B

Given:

Volume (V) of the cylinder = 4851 cm³

Curved Surface Area (CSA) = 462 cm²

The cylinder is generated by rotating a rectangle about its length by 360°.

Formula Used:

Volume of the cylinder = $$\pi r^2 h$$​​

Curved Surface Area (CSA) of the cylinder = 2πrh

The rectangle's Length (L) becomes the height of the cylinder, and the Width (W) becomes the radius of the cylinder.

Solution:

From the CSA formula:

$$2\pi r h = 462 \\ \ \\ \pi r h = 231 \quad \text{(1)}$$​​

From the Volume formula:

$$\pi r^2 h = 4851 \quad \text{(2)}$$​​

Dividing equation (2) by equation (1)

$$\frac{\pi r^2 h}{\pi r h} = \frac{4851}{231}\\ \ \\ r = 21 \, \text{cm}$$​​

Substitute r = 21 cm into equation (1) ;

$$\pi \times 21 \times h = 231$$​​

​$$\frac{22}{7} \times 21 \times h = 231$$​​

​$$h = \frac{231}{66} = 3.5 \, \text{cm}$$​​

The dimensions of the rectangle:

Length (L)= 3.5 cm

Width (W)= 21 cm

Perimeter of rectangle:

P = 2(L+ W) = 2(3.5 + 21) = 2 × 24.5=49 cm