Question

A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter 7 cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are 24 cm × 12 cm × 17 cm.

(i) Find the surface area of the bulb.   [1]

(ii) What could be the maximum diameter of the bulb if at least 1 cm space is left from each side?   [1]

(iii) (a) Find the area of the fabric used ifthere is a fold of 2 cm on top and bottom edges.   [2]

OR

(iii) (b) Find the space available inside the lamp.   [2]

Answer 1

(i) Surface area of bulb = 4πr²

= `4 xx 22/7 xx 7/2 xx 7/2`   ...[d = 7]

= 22 × 7

= 154 cm² 

(ii) Internal dimension 24 × 12 × 17

Length = 24 – (1 cm + 1 cm) = 22 cm

Width = 12 – (1 cm + 1 cm) = 10 cm

Height = 17 – (1 cm + 1 cm) = 15 cm

Maximum diameter = Minimum of (22 cm, 10 cm, 15 cm) = 10 cm

(iii) (a) Required height = 17 cm + 2 cm + 2 cm = 21 cm

Fabric required = 2(l + b) × h

Area of 4 walls = 2(24 + 12) × 21

= 72 × 21

= 1512 cm²

OR

(iii) (b) Space available = l × b × h

Volume = 24 × 12 × 17

= 4896 cm³