Question

A heap of rice is in the form of cone of base diameter 24m and height 3.5. Find the volume of the rice . How much canvas cloth is required to just cover the heap.

Answer 1

Find the radius:

Radius = Diameter ÷ 2

Radius = 24 ÷ 2 = 12 m

Find the volume of the rice:

Volume of a cone = 1/3 πr²h

Volume of the rice = 1/3 π (12)² (3.5) = 528 m³

Find the slanted height:

a² + b² = c²

3.5² + 12² = c²

c² = 12²+ 3.5²

c² = 156.25

c = √156.25

c = 12.5 m

Find the curved surface area:

Curved surface area = πrl

Curved surface area = π(12)(12.5) = 471.4 m²

Answer: The volume is  528 m³ and 471.4 m² of canvas cloth is needed to cover the heap.

Answer 2

Shape of heap of rice is a cone.

Base diameter = 24 m ∴ Base radius = 12 m

Height of the cone = 3.5 m = 72m

Part 1: Compute Volume of Cone

Volume of cone = 13 πr2h

Volume = 13 × 227 × 12 × 12 × 72 = 528 m3

Part 2: Compute Curved Surface Area (CSA) of Cone

Area of canvas cloth required to cover the heap = Curved surface area of cone = πrl

l - slant height of the cone

l = h2+r2−−−−−−√ = (72)2+(242)2−−−−−−−−−−√ = 12 49+576−−−−−−−√

l = 126–√25 = 252m

CSA = 227 × 12 × 252 = 33007 = 471.42 sq m