Q) A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

(Q 21- 30/3/3 – CBSE 2026 Question Paper)

Ans:

Step 1: We have following data:

Radius of the hemisphere, R_H = 7 cm

Height of the hemisphere, H_H = 7 cm (height is same as radius)

Radius of the cone, R_C = 7 cm

Step 2: Height of the cone = Total height of the toy – Radius of the hemisphere

= 31 – 7 = 24 cm

∴ Slant height, L = √[(H2 + R2)] = √[(24)2 + (7)2]

∴ L = √(576 + 49) = √625 = 25 cm

Step 3: ∴ Curved surface area of conical top, CSA_CONE = π R L

= π (7) (25) = 175 π

Step 4: Curved surface area of hemisphere, CSA_HEMI

= 2 π R ²

= 2 π (7) ² = 98 π

Step 5: Total surface area of the toy = Curved surface area of conical top + Curved surface area of hemisphere

= 175 π + 98 π = 273 π

= 273 x = 39 x 22 = 858 cm ²

Therefore, the total surface area of the toy is 858 cm ².

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