For a cuboid with length (l), breadth (b) and height (h), which of the following statements are true? (i) Total surface area of the cuboid (ii) Diagonal of the cuboid has a length of

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Solution

Q.
For a cuboid with length (l), breadth (b) and height (h), which of the following statements are true

(i) Total surface area of the cuboid $= 2 (l b + b h + l h) square units .$

(ii) Diagonal of the cuboid has a length of $\sqrt{l^{2} + b^{2} + h^{2}} units .$

(iii) If the cuboid was a room, the area of its walls would be $(2 l + 2 b + 2 h) square units .$

(iv) All cuboids are cube.

Choose the correct option from the following:

1 (i) and (ii)

2 (ii) and (iii)

3 (i) and (iv)

4 (ii) and (iv)

Ans.
(1)

(i) Total surface area $= S u m o f a r e a s o f a l l f a c e s = l b + b h + l h + b h + l h + l b = 2 (l b + b h + l h)$

(ii) Diagonal length $= \sqrt{l^{2} + b^{2} + h^{2}}$

The diagonal joins two opposite vertices of the cuboid.

(iii) Sum of the areas of the walls $= l h + b h + l h + b h = 2 h (l + b)$

(iv) All cubes are cuboid but all cuboids are not cube.

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