Question

A bucket has top diameter of 30cm and 20cm respectively. Find the volume of the bucket of Dept 12cm. Also find the cost of tin sheet use door making the bucket at the rate of 10 paise per cm sq

Answer 1

Let the radius of the top part be 'R' and radius of the bottom part be 'r' respectively.

Diameter (Top) = 40 cm 
Radius (R) = 40/2 = 20 cm 
10 cm = 1 dm 
20 cm = 2dm

Diameter (Bottom) = 20 cm
Radius (r) = 20/2 = 10 cm 
10 cm = 1 dm

Height = 12 cm = 1.2 dm

Slant height ('l') = √H² + (R - r)²
= √(1.2)² + (2 - 1)²
= √1.44 + 1
= √2.44
= 1.56
So, slant height (l) is 1.56 dm

Area of the tin sheet used for bucket = Curved surface area of the bucket + Area of the base
= π(R + r)*l + πr²
⇒ 3.14*(2 + 1)*1.56 + 3.14*1²
⇒(3.14*3*1.56) + 3.14
⇒ 14.6952 + 3.14
⇒ 17.8352 sq dm
CSA of the tin sheet used = 17.8352 sq dm
Rate of tin sheet = Rs. 1.2 per sq dm
Total cost of the tin sheet used for making the bucket = 17.8352*1.2
= Rs. 21.40
Answer.
Volume = 1/3πh(R² + r² + R*r)
= 1/3*3.14*1.2*(2² + 1² + 2*1)
= 1/3*3.14*1.2*7
= 26.376/3
Volume = 8.792 cu dm