Question

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.   [1]

(ii) Find the volume of Rubik’s cube if the length of the edge is 7 cm.   [1]

(iii) (a) What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm?   [2]

OR

(iii) (b) If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid.   [2]

Answer 1

(i) Length of diagonal of Rubik’s cube:

Given edge = 6 cm

Diagonal of a cube = `sqrt(3)a`

= `sqrt(3) xx 6`

= `6sqrt(3)  cm`

(ii) Volume of Rubik’s cube:

Given edge = 7 cm

Volume = a³ = 7³

= 7 × 7 × 7

= 343 cm³

(iii) (a) Curved surface area of hemisphere

Given radius (r) = 7 cm

CSA of hemisphere = 2πr²

= `2 xx 22/7 xx 7 xx 7`

= 2 × 22 × 7

= 308 cm²

OR

(iii) (b) Surface area of resulting cuboid.

When two cubes of edges 4 cm are joined end-to-end.

Length (l) = 4 + 4 = 8 cm

Breadth (b) = 4 cm

Height (h) = 4 cm

Total surface area (TSA) of cuboid

= 2(lb + bh + hl)

= 2(8(4) + 4(4) + 4(8))

= 2(32 + 16 + 32)

= 2(80)

TSA = 160 cm²