Question

if height of the cylinder is equal to its diameter and volume is 58212cm square,then find the curved surface area and total surface area of the cylinder.

Answer 1

Let r be the radius of base and h be the hight of cylinder.
Now,r=h/2
Now volume =58212cm³
=πr²h=58212cm³
=22/7×h²/4×h=58212
=h=42cm
Now r= h/2=42/2=21 r
Now CSA=2πrh=2×22/7×21×42=5544cm²
TSA=2πr(h+r)=2×22/7×21×(63)=8316cm²

Answer 2

question ask ,
h = 2r ------(1)

volume of cylinder = πr² h
58212 = 22/7 × r²(2r) { from eqn (1)

58212 = 44/7 × r³

r³ = 7 × 58212/44 = 7× 5292/4 = 7×1323
= 7 × 7 × 189
= 7 × 7 × 7 × 3 × 3 × 3

so, r = 21 cm and h = 2r = 42 cm

now, curve surface area = 2πrh
= 2 × 22/7 × 21 × 42
= 44 × 126
=5544 cm²

total surface area = 2πr² + 2πrh
= 2πr( r + h)
=2 ×22/7 × 21 × (21+42)
= 44 ×3 × 63 cm²
=8316 cm²