The volume of a cuboid is $448 {c m}^{3}$ . Its height is $7 c m$ and the base is a square. Find
(i) a side of the square base
(ii) surface area of the cuboid

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Solution

Given
Volume of cuboid $= 448 {c m}^{3}$
Height of cuboid $= 7 c m$
And the base is a square.

(i) We know that,
Volume of cuboid $=$ Base area $\times$ Height
$\Rightarrow 448 = (s i d e)^{2} \times 7 \Rightarrow (s i d e)^{2} = \frac{448}{7} = 64 \Rightarrow s i d e = \sqrt{64} = 8 c m$

(ii) Surface area of the cuboid $= 2 (l b + b h + h l) = 2 (8 \times 8 + 8 \times 7 + 7 \times 8) {c m}^{2} = 352 {c m}^{2}$

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The volume of a cuboid is 448cm3. Its height is 7cm and the base is a square. Find(i) a side of the square base(ii) surface area of the cuboid

GivenVolume of cuboid =448cm3Height of cuboid =7cmAnd the base is a square.(i) We know that, Volume of cuboid = Base area × Height⇒448=(side)2×7⇒(side)2=4487=64⇒side=√64=8cm(ii) Surface area of the cuboid =2(lb+bh+hl)=2(8×8+8×7+7×8)cm2=352cm2

The volume of a cuboid is $448 {c m}^{3}$ . Its height is $7 c m$ and the base is a square. Find
(i) a side of the square base
(ii) surface area of the cuboid