Q) On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik’s cube and a strawberry ice-cream for you.
Based on the information given above, answer the following questions:
(i) Find the length of the diagonal of Rubik’s cube if each edge measures 6 cm.
(ii) Find the volume of Rubik’s cube if the length of the edge is 7 cm.
(iii) (a) What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm?
(iii) (b) If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid.
[Q 37 – 30/2/2 – CBSE 2026 Question Paper]
Ans:
(i) Diagonal length of Rubik’s cube:
Given: Edge of cube = 6 cm
We know that the diagonal of a cube = √3 × edge
∴ the diagonal length = √3 × 6
= 6√3 cm ≈ 10.39 cm
Therefore, the length of the diagonal of Rubik’s cube is 10.39 cm.
(ii) Volume of Rubik’s cube:
Given: Edge of cube = 7 cm
We know that the volume of a cube = (edge)3
∴ Volume of given cube = 73 = 343 cm3
Therefore, the volume of the Rubik’s cube is 343 cm3.
(iii)(a) Curved surface area of hemisphere:
Given: Radius = 7 cm
We know that the Curved surface area of a hemishephere = 2 π r 2
∴ CSA of given hemisphere = 2 × π × (7) 2
= 2 × (22 / 7) × 7 x 7
= 2 x 22 x 7 = 308 cm2
Therefore, the curved surface area of hemisphere is 308 cm 2
(iii)(b) Surface area of cuboid formed by joining two cubes:
Given: edge of each cube = 4 cm
When 2 cubes are joined end-to-end, a cuboid of following dimensions will get formed:
Length, L = 8 cm (combined length of 2 cubes)
Breadth, B = 4 cm (breadth of 1 cube)
Height, H = 4 cm (height of 1 cube)
We know that the surface area of the cuboid = 2 (LB + BH + HL)
∴ The surface area of the resulting cuboid = 2 (8 x 4 + 4 x 4 + 4 x 8)
= 2 (32 + 16 + 32)
= 2 × 80 = 160 cm2
Therefore, the curved surface area of cuboid is 160 cm 2
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