Question

If the curved surface area of a right circular cylinder whose base radius and height are equal is 72piecm^2, then the diameter of the base is​

Answer 1

Answer:

Diameter of base of cylinder is 12 cm.

Step-by-step explanation:

Given :

• Curved surface area of a right circular cylinder is 72π cm².
• Radius and height of cylinder are equal.

To find :

• Diameter of base of cylinder.

Solution :-

We know,

Curved surface area of cylinder = 2πrh

[Where, r is radius and h is height of cylinder]

Put all values :

$\longrightarrow$ 72π = 2 × π × r × h

• Radius and height are equal.

$\longrightarrow$ 72π = 2π × r × r

$\longrightarrow$ 72π = 2π × r²

$\sf \longrightarrow \dfrac{72 \: \cancel{\pi}}{2 \: \cancel{\pi}}$ = r²

$\longrightarrow$ 36 = r²

$\longrightarrow$ √36 = r

$\longrightarrow$ r = 6

Radius of cylinder is 6 cm.

Now,

Diameter = 2 × radius

$\longrightarrow$ Diameter = 2 × 6

$\longrightarrow$ Diameter = 12

Therefore,

Diameter of base of cylinder is 12 cm.

Answer 2

Given :-

CSA of cylinder = 72π cm².

Height and radii are equal

To Find :-

Diameter

Solution :-

At first we have to know about the CSA of cylinder

CSA = 2πrh

Here,

R is the radius

h is the height

Since, radius and height are of same size, So,

r = h

Let height be also r

$\sf 72\pi = 2\pi\times r \times r$

• Cancelling π

$\sf 72 = 2 \times r^{2}$

$\sf \dfrac{72}{2} = r^{2}$

$\sf 36 = r^{2}$

$\sf \sqrt{36}=r$

$\sf 6 = r$

Since,

Diameter = 2  ×  radius

Diameter = 2  × 6

Diameter = 12 cm

V E R I F I C A T I O N :

$\tt 72\pi = 2 \pi \times 6 \times 6$

$\tt 72\pi = 2\pi \times 36$

• Cancelling   π

$\sf 72 = 2 \times 36$

$\tt 72 = 72$