Question

A right-angled triangle PQR where ∠Q = 90° is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle

Answer 1

In the Right Triangle

QP² = PR² – QR²

= 20² – 16² 

= 400 – 256

= 144

QP = `sqrt(144)` = 12 cm

When PQ is rotated r = 12, l = 20

C.S.A of the cone = πrl sq. units

= π × 12 × 20 cm²

= 240π cm²

When QR is rotated r = 16, l = 20

C.S.A of the cone = nrl sq. units

= π × 16 × 20

= 320π cm²

C.S.A. of a cone when rotated about QR is larger.