A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is 1/4 of its height. The surface area of the solid is : (Take π = 22\7 )

Explanation:

Let radius of the cylinder be r cm and height = h cm

Then, r = h\8 given

and h = 35 – 2r = 35 – 2 × h\8

=> h + h\4 = 35 => 5h\4 = 35

=> h = 35×4\5 = 28 cm

∴ r = h\8 = 28\8 = 7\2 cm

∴ Radius of the hemisphere = 7\2 cm

Total surface of area the solid

= (2 πrh + 2 \times 2 πr^2 )sq. cm.

= 2 π r (h + 2r) sq. cm.

= 2×22\7×7\2×(28+2×7\2)sq.cm

= 2 × 22\7 × 7\2 × 35 sq.cm

= 770 sq.cm