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Question
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) the total surface area of the cuboid.
(iii) the total surface area of the cube.
(iv) which of these two has a greater surface and by how much?
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Solution
Edge of a cube = 6 cm
Volume = a3 = (6)3 = 216 cm3
Dimensions of a cuboid = 4 cm x x cm x 15 cm
Volume = 60x cm3
The volume of both is equal
(i) ∴ `60x = 216 ⇒ x = 216/60 = 36/10`
∴ x = 3.6 cm
(ii) Total surface area of cuboid
= 2[lb + bh + hl]
= `2[4 xx 3.6 + 3.6 xx 15 + 15 xx 4]` cm2
= 2[14.4 + 54.0 + 60] cm2
= `128.4 xx 2 = 256.8` cm2
(iii) Total surface area of cube
= `6a^2 = 6(6)^2 = 6 xx 36 = 216` cm2
(iv) Difference of surface areas = 256.8 - 216
= 40.8 cm2
∴ Surface area of cuboid is greater
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