Question

A solid cylinder has a surface area 462 cm. It's Curved surface area is one third of the total surface area. Find the height of the cylinder.

Answer 1

Answer:

TOTAL SURFACE AREA OF THE CYLINDER(TSA)=462CM²

CURVED SURFACE=1/3 OF TSA

=1/3 X 462

=154CM²

 AREA OF EACH CIRCLE=(462-154)/2

=154CM²

PI*R²=154

R²=49

R=7

2PI*R*H=154

H=154*7/22*7

H=3.5

VOLUME=PI*R²*H=22/7*49*35/10

VOLUME=539CM³

or

We have Total Surface Area of cylinder

= 2πr( h + r ) or 2πrh + 2πr²

2πrh + 2πr² = 462 cm² _(i)

Where,

Curved Surface Area = ⅓ Total Surface Area

2πrh = ⅓ × 462 cm²

2πrh = 154 cm²

Substituting value of 2πrh in eq (i),

154 cm² + 2πr² = 462 cm²

2πr² = 462 - 154 cm² = 308 cm²

r² = 308/2π

r² = 308 × 1/2 × 7/22 cm²

r² = 28 × 1/2 × 7/2 cm²

r = √49 cm² = 7 cm

Substituting value of r in 2πrh

2πrh = 154 cm²

h = 154/2πr

h = 154 × 1/2 × 7/22 × 1/7 cm

h = 7/2 cm

Volume of cylinder = πr²h

= 22/7 × 7² × 7/2 cm³

= 539 cm³