Question

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.

Answer 1

Soln:

Given:

Perimeters of ends of frustum right circular cone are 44 cm and 33 cm

Height of the frustum cone = 16 cm

Perimeter = 2Πr2Πr

2Πr12Πr1 = 44 ; 2Πr22Πr2 = 33

r1r1 = 7 cm ; r2r2 = 5025 cm

Let the slant height of frustum right circular cone be L

L = √(r1−r2)2+h2(r1−r2)2+h2−−−−−−−−−−−−√

L = √(7−5.25)2+162(7−5.25)2+162−−−−−−−−−−−−−−√

L = 16.1 cm

∴∴ Slant height of the frustum cone = 20.37 cm

Curved surface area of the frustum cone = Π(r1+r2)LΠ(r1+r2)L

= Π(7+5.25)16.1Π(7+5.25)16.1

Curved surface area of the frustum cone = 619.65 cm3cm3

Volume of the frustum cone = 13Π(r21+r22+r1r2)h13Π(r21+r22+r1r2)h

= 13Π(72+5.252+7×5.25)×1613Π(72+5.252+7×5.25)×16

= 1898.56 cm3cm3

∴∴ volume of the cone = 1898.56 cm3cm3

Total surface area of the frustum cone = Π(r1+r2)L+Πr21+Πr22Π(r1+r2)L+Πr21+Πr22

= Π(7+5.25)×16.1+Π72+Π5.252Π(7+5.25)×16.1+Π72+Π5.252

= Π(7+5.25)×16.1+Π(72+5.252)Π(7+5.25)×16.1+Π(72+5.252)

= 860.27 cm2cm2

∴∴ total surface area of the frustum cone = 860.27 cm2cm2