Question

A frustum of a right circular cone has a diameter of base 20cm of top 12cm and height 3cm .Find the area of its whole surface and volume

Answer 1

Sol:

Given base diameter of cone (d1)(d1)= 20cm

Radius (r1)(r1) = 202cm=10cm202cm=10cm

Top diameter of Cone (d2)(d2) = 12 cm

Radius (r2)(r2) = 122cm=6cm122cm=6cm

Height of the cone (h)= 3cm

Volume of the frustum right circular cone = Π3(r21+r22+r1r2)hΠ3(r21+r22+r1r2)h

= Π3(102+62+10×6)3Π3(102+62+10×6)3

=616 cm3cm3

Let ‘L’ be the slant height of cone

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

=>L = √(10−6)2+32(10−6)2+32−−−−−−−−−−−√

=>L = √2525−−√

=>L = 5 cm

∴∴ Slant height of cone (L)(L)= 5 cm

Total surface area of the cone =Π(r1+r2)×L+Π×r21+Pi×r22Π(r1+r2)×L+Π×r21+Pi×r22

= Π(10+6)×5+Π×102+Pi×62Π(10+6)×5+Π×102+Pi×62

= Π(80+100+36)Π(80+100+36)

= Π(216)Π(216)

= 678.85cm2678.85cm2

∴∴

Total surface area of the cone = 678.85 cm2cm2