Rasheed got a playing top ( lattu ) as his birthday present , which surprisingly had no colour on it . He wanted to colour it with his crayons . The top is shaped like a cone surmounted by a hemisphere ( see Fig 13 . 6 ) . The entire top is 5 cm in height and the diameter of the top is 3 . 5 cm . Find the area he has to colour
please solve it step by step with full explanation.
Answers
Answer:
39.55 cm²
Step-by-step explanation:
Surface area to colour = Surface area of hemisphere + Surface area of cone
i) Surface area of hemisphere:
r= d/2 = 3.5/2
Surface area = 2πr² = 2 * 22/7 * (3.5/2)²
= 19.25 cm²
ii) Curved surface area of cone:
Surface area= πrl
Here, r = 3.5/2 = 1.75 cm
Height of cone = Height of top - radius
= 5-1.75 = 3.25 cm
l² = h²+r²
l² = (3.25)²+(1.75)²
l² = 10.56 + 3.0625
l² = 13.6225
l = √13.6225
l = 3.69 cm
∴ area = πrl
= 22/7 * 3.5/2 * 3.69
= 11 * 0.5 * 3.69
= 20.3 cm²
Hence surface area of top = Surface area of hemisphere + Surface
area of cone
= 19.25 + 20.3
= 39.55 cm²
HOPE THIS HELPS ^_^
REFER TO THE ATTACHMENT FOR BETTER UNDERSTANDING
