Question

5. Four metal cubes with edges 9 cm, 6 cm, 4 cm and 2 cm are melted together and a single new
cube is formed with a wastage 17 cm3. Find the total surface area of the new cube.​

Answer 1

Answer : 600 cm squared.

Here,

(Volume of four small cubes) - (wasted volume) = Volume of large cube.

Let the side of Larger cube formed be 's' cm.

Hence,

$(9×9×9) + (6×6×6) + (4×4×4) + (2×2×2) - 17 = {s}^{3}$

$→ \: 729 + 216 + 64 + 8 - 17 = {s}^{3}$

$→1017 - 17 = {s}^{3}$

$→1000 = {s}^{3}$

$→s = 10 \: cm$

Hence one side of larger cube = 10 cm

Therefore, it's total surface area

= 6 × side^2

$→TSA = 6 \times {10}^{2} \\ →TSA = 600 \: {cm}^{2}$

Hope this helps :)