Q) In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm.

Based on the above, answer the following questions:

(i) Find the area of the base of the cylindrical cup.

(ii) (a) What is the capacity of the hemispherical cup?

OR

(ii) (b) Find the capacity of the cylindrical cup.

(iii) What is the curved surface area of the cylindrical cup?

Ans: 

VIDEO SOLUTION

STEP BY STEP SOLUTION

(i) Area of base of the cylindrical cup:

We know that, area of base of the cylindrical cup =

Radius of the cylindrical cup = cm

area of base of cylindrical cup = x x

= 11 x = 38.5 cm²

Therefore, Area of base of the cylindrical cup is 38.5 cm²

(ii) (a) capacity of the hemispherical cup:

We know that, capacity of the hemispherical cup =

Since, the radius of the hemispherical cup = cm

the capacity of hemispherical cup = x x x x

= 11 x 21 x  = = 2425.5 cm³

Therefore, Capacity of the hemispherical cup is 2425.3 cm³ 

(ii) (b) Capacity of the cylindrical cup:

We know that, the capacity of the cylindrical cup =

Given that the radius of the cylindrical cup = cm and the height of the cup is 14 cm

the capacity of the cylindrical cup = x x x 14

= 11 x 7 x 7 = 539 cm³

Therefore, Capacity of the cylindrical cup is 539 cm³

(iii) curved surface area of the cylindrical cup:

We know that the curved surface area of the cylindrical cup =

Given that the radius of the cylindrical cup = cm and the height of the cup is 14 cm

the curved surface area of the cylindrical cup = 2 x x x 14

= 2 x 11 x 14 = 308 cm²

Therefore, curved surface area of the cylindrical cup is 308 cm²