The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 Π

1.	The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 Π cm. If the depth is 14 cm, then find its volume.
Answer» Perimeter of upper end = 44 cm Perimeter of lower end = 8.4 Π cm Height of frustum cone =14 cm Now we have to find the volume of frustum cone Volume of the frustum cone = (1/3)Πh (R²+ r² + R r) 2Π R = 44 2x(22/7)xR = 44 R = 44x(1/2)x(7/22) R = 2x(1/2)x(7) R =7 2Π r =8.4 Π 2xΠxr =8.4 Π r =8.4 Πx(1/2Π) r = 4.2 Volume of the frustum cone = (1/3)x(22/7)x(14)(7²+ 4.2² + 7(4.2))= (44/3)(49+ 29.4+ 17.64) = (44/3)(96.04) = (44)(32.013) = 1408.57 cm³ Volume of the frustum cone = 1408.57 cm³

The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 Π cm. If the depth is 14 cm, then find its volume.

Answer»

Perimeter of upper end = 44 cm

Perimeter of lower end = 8.4 Π cm

Height of frustum cone =14 cm

Now we have to find the volume of frustum cone

Volume of the frustum cone = (1/3)Πh (R²+ r² + R r)

2Π R = 44

2x(22/7)xR = 44

R = 44x(1/2)x(7/22)

R = 2x(1/2)x(7)

R =7

2Π r =8.4 Π

2xΠxr =8.4 Π

r =8.4 Πx(1/2Π)

r = 4.2

Volume of the frustum cone = (1/3)x(22/7)x(14)(7²+ 4.2² + 7(4.2))= (44/3)(49+ 29.4+ 17.64)

= (44/3)(96.04)

= (44)(32.013)

= 1408.57 cm³

Volume of the frustum cone = 1408.57 cm³