Question

find the base radius of a right circular cylinder whose whole surface is 231cm and the curved surface is 2/3 of the whole surface
​

Answer 1

The base radius of the cylinder is 3.5 cm

Step-by-step explanation:

The Total Surface Area of the right circular cylinder is

231 cm2 = 2πrh + 2πr² ………….(1)

The curved surface area of the cylinder is 2πrh

Given:

The curved surface area is 2/3 of TSA

Thus;

2/3 × (2πrh + 2πr²) = 2πrh

2/3 × 2πr (h + r ) = h × 2πr

Diving both sides by 2πr

2/3 (h + r) = h

2h + 2r = 3h  

h = 2r …………………………(2)

Eq 1 states:

2πrh + 2πr² = 231  

2πr × (h + r) = 231

But h = 2r

Substituting the value of Eq. 2 in Eq. 1

2πr × (2 r + r) = 231

2πr × 3r = 231

6 × 22/7 × r2 = 231

r2 = 12.25

r = 3.5 cm

Thus, the base radius of the cylinder is 3.5 cm