A man installed an overhead tank on his terrace having a cylindrical s

1.	A man installed an overhead tank on his terrace having a cylindrical shape surmounted by hemisphere. The ratio of radius of hemisphere to the height of cylinder is 1 : 4 . If he wants to paint the outer surface of the tank completely, find the cost of painting it at the rate of Rs. 0.1/m2, given the circumference of the base of hemisphere is 88 m.1. 7292. 6163. 7204. 500
Answer» Correct Answer - Option 2 : 616 Given : Circumference of base of hemisphere = 88 m Radius of hemisphere : height of cylinder = 1 : 4 Cost of painting = Rs. 2 per meter sq. Formula Used: Area of paint = curved surface area of hemisphere + curved surface area of cylinder Cost of painting = total curved surface area × cost of painting Calculations: Let the radius of hemisphere and height of cylinder be r and h respectively ⇒ Circumference of base of hemisphere = 2πr = 88 m ⇒ r = 14 m ⇒Height of cylinder = 14 × 4 ⇒ h = 56 m ⇒CSA of hemisphere = 2πr² = 2 π × 14 ×14 ⇒CSA of hemisphere = 1232 m² ⇒ CSA of cylinder = 2πrh= 2π × 14× 56 ⇒ CSA of cylinder = 4928 m² ⇒ Total curved surface area = (4928 + 1232) m² ⇒ Total curved surface area = 6160 m² ⇒Cost of painting = Rs. 6160 × 0.1 ⇒ Cost of painting = Rs. 616 ∴ The cost of painting is Rs. 616.

A man installed an overhead tank on his terrace having a cylindrical shape surmounted by hemisphere. The ratio of radius of hemisphere to the height of cylinder is 1 : 4 . If he wants to paint the outer surface of the tank completely, find the cost of painting it at the rate of Rs. 0.1/m2, given the circumference of the base of hemisphere is 88 m.1. 7292. 6163. 7204. 500

Answer» Correct Answer - Option 2 : 616

Given :

Circumference of base of hemisphere = 88 m

Radius of hemisphere : height of cylinder = 1 : 4

Cost of painting = Rs. 2 per meter sq.

Formula Used:

Area of paint = curved surface area of hemisphere + curved surface area of cylinder

Cost of painting = total curved surface area × cost of painting

Calculations:

Let the radius of hemisphere and height of cylinder be r and h respectively

⇒ Circumference of base of hemisphere = 2πr = 88 m

⇒ r = 14 m

⇒Height of cylinder = 14 × 4

⇒ h = 56 m

⇒CSA of hemisphere = 2πr² = 2 π × 14 ×14

⇒CSA of hemisphere = 1232 m²

⇒ CSA of cylinder = 2πrh= 2π × 14× 56

⇒ CSA of cylinder = 4928 m²

⇒ Total curved surface area = (4928 + 1232) m²

⇒ Total curved surface area = 6160 m²

⇒Cost of painting = Rs. 6160 × 0.1

⇒ Cost of painting = Rs. 616

∴ The cost of painting is Rs. 616.