Q) 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 24cm x 12cm x 17cm
(i) Find the surface area of the bulb.
(ii) What could be the maximum diameter of the bulb if at least 1 cm space is left from each side?
(iii) Find the area of the fabric used if there is a fold of 2 cm on top and bottom edges.
(iv) Find the space available inside the lamp.

(Q 38 – 30/5/2 – CBSE 2026 Question Paper)

Ans:

(i) Surface area of the bulb:

∵ Given the diameter of spherical bulb = 7 cm

∴ Radius of the bulb = = 3.5 cm

∵ Curved Surface area of sphere = 4 π r ²

∴ CSA of bulb = 4

= 22 x 7 = 154 cm ²

Therefore, surface area of the bulb is 154 cm ²

(ii) Maximum diameter of the bulb:

Bulb has to fit in the cuboid box, its maximum dimension will be limited by lowest dimension of the cuboid box.

∵ given the cuboid has dimensions of 24 cm x 12 cm x 17 cm

∴ Lowest dimension (Width of 12 cm) will be deciding dimension

∵ We need to leave 1 cm from each side, hence we need to subtract 2 cm from each side.

∴ maximum space available for bulb can be 12 – 2 = 10 cm

Therefore, Bulb’s maximum diameter can be 10 cm.

(iii) Area of the fabric:

Since the lamp is open at the top and bottom, meaning the fabric will cover only the Lateral Surface Area (LSA) of the cuboid.

Additionally, we must account for a 2 cm fold at both the top and bottom edges.

∴ Effective Height = Original height + fold at the top and bottom

= 17 + 2 + 2 = 21 cm

Length of the fabric = Perimeter of the cuboid box

= 2(length + width) = 2 (24 + 12)

= 2 x 36 = 72 cm

∴ Area of the fabric used = 21 x 72 = 1512 cm ²

Therefore, Area of the fabric used 1,512 cm ².

(iv) Space inside the lamp:

It is given in the question that lamp has cuboidal shape with a lamp inside

Size of lamp is 24 cm x 12 cm x 17 cm

∴ Total volume inside lamp

= 24 x 12 x 17 = 4896 cm ³

Volume covered by bulb

= π r ³

=  

= = 179.67 cm ³

Net volume inside the box = Total volume inside box – volume taken up by bulb

= 4896 – 179.67 = 4716.33 cm ³

Therefore, the space available inside the lamp is 4,716.33 cm ³

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