Question

The lateral surface area of a cuboid is 224 cm2. Its height is 7 cm and the base is a
square. Find
(i) a side of the square, and (ii) the volume of the cuboid.
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Answer 1

Answer:

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Step-by-step explanation:

Given height=7cm

Lateral surface area of cuboid=

$lateral \: surface \: are \: of \: cuboid \: = 2(l + b ) \times h$

$(1) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2(l + b) \times 7 = 224 \\ (l + b) = 244 \div 14 \\ = 16cm \\ \\ but \: l = b \:( as \: the \: side \: if \: a \: cuboid \: is \: a \: square \: ) \\ so \\ 2 \times side \: = 16cm \\ side = 16 \div 2 = 8cm \\ \\ (2) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: volume \: of \: cuboid \: = l \times b \times h = 8 \times 8 \times 7 = {448cm}^{3}$