CASE STUDY QUESTION 33-Class X-Maths

CASE STUDY QUESTION 33-Class X-Maths

Rasheed is very happy for his birthday celebration. He got lot of birthday gifts in his party. Out of all birthday gifts, he liked a playing top (lattu) most, 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 the below figure). The entire top is 5 cm in height and the diameter of the top is 3.5 cm.

(a) What is height of the cone?
(i) 5 cm (b) 3 cm (c) 3.25 cm (d) 4 cm

Sol: Height of the cone = height of the top – height (radius) of the hemispherical part
= 5 – (3.5/2) = 5 – 1.75
= 3.25 cm

(b) What is slant height of the cone?
(i) 5 cm (b) 3.7 cm (c) 3.25 cm (d) 4 cm

(c) What is the Curved Surface Area of the cone?
(i) 19.5 cm²
(ii) 20.35 cm²
(iii) 20.5 cm²
(iv) 19.25 cm²

(d) What is the Curved Surface Area of the hemisphere?
(i) 19.5 cm²
(ii) 20.35 cm²
(iii) 20.5 cm²
(iv) 19.25 cm²

(e) What is the Total Surface Area of the toy?
(i) 39.6 cm²
(ii) 39.35 cm²
(iii) 39.5 cm²
(iv) 39.85 cm²

Sol: Total Surface Area of the toy = CSA of hemisphere + CSA of cone
= 19.25 + 20.35 cm²
= 39.6 cm²