Question

A right triangle, whose sides are 6 cm, 8 cm and 10 cm is made to revolve about its side 8 cm. Find the volume and total surface area of the cone so formed. (use π = 3.14)

Answer 1

Given:

Right triangle with sides 6 cm, 8 cm, and 10 cm (right-angled).

The triangle is revolved about its sideby  8 cm.

Use π = 3.14.

Identify the cone dimensions when the right triangle is revolved about the leg 8 cm:

Height of cone, h = 8 cm.

Radius of base, r = 6 cm.

Slant height, l = 10 cm.

Formulae (from a cone obtained by revolving a right triangle):

Volume: V = `(1/3) π r^2 h.`

Curved (lateral) surface area: A_c = π r l.

Total surface area: 

A_t = A_c + base area

= πrl + π r² = π r (l + r).

Compute the volume:

r2 = 6² = 36

r² × h

= 36 × 8

= 288

V = `(1/3) × 3.14 × 288`

= 3.14 × 96 

= 301.44 cm³

Compute the total surface area:

= l + r 

= 10 + 6

= 16

A_t = π × r × (l + r)

= 3.14 × 6 × 16

= 3.14 × 96 

= 301.44 cm²