Question

a solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. the radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 16656cm³. find the height of the toy . also find the cost of painting the hemisphere part of the toy at the rate of ₹10 per cm².(use π=22/7)​

Answer 1

Correct Question:-

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. the radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 5/6cm³. find the height of the toy . also find the cost of painting the hemisphere part of the toy at the rate of ₹10 per cm².(use π=22/7)

Required Answer:-

Given:-

• Radius of hemisphere = radius of cone = 3.5 cm
• Volume of  total wood used in making a toy = 166 5/6 = 1001/6 cm^3

To Find:-

• Height of the toy
• The cost of painting the hemisphere part of the toy.

Solution:-

We know that:-

Volume of hemisphere = (2/3) π(r)^3 cube units

And,

Volume of cone = (1/3)πr^2h

Where,

• r is radius and h is the height.

According to the question:-

Volume of  total wood used in making a toy = volume of hemisphere + volume of cone

Volume of total wood = (2/3) × πr^3 + (1/3)πr^2h

=> 1001/6 = (2/3) ×22/7×(3.5)^3 + (1/3) ×22/7×(3.5) ^2×h

=> 1001/6 = 1/3×22/7(2×42.875 + 12.25h)

=> (1001×3×7)/(6×22) = 85.75 + 12.25h

=> 21021/132 = 85.75 + 12.25h

=> 12.25h = 159.25 - 85.75

=> 12.25h = 73.5

=> h = 73.5/12.25

=> h = 6

Hence, height of the cone(h) = 6cm

Now,

Height of the toy = Height of a cone + Height of a hemisphere

=> Height of the toy = 6 +3.5 = 9.5 cm

Again,

Curved surface area of hemisphere = 2πr²

=> CSA of hemisphere = 2 ×( 22/7) × 3.5 × 3.5

=> CSA of the hemisphere = 77 cm²

We were given:-

• Rate of painting the hemispherical part of the toy = ₹ 10 per cm^2

Therefore,

Cost of painting the hemispherical part of the toy = 77 × 10 =  ₹ 770 .

○Hence, the Height of the toy is 9.5 cm & Cost of painting the hemispherical part of the toy is  ₹ 770.