Question

A cuboidal box of dimensions 21cm x 14cm x 7cm is made up of cardboard. from the top face two circles of diameter 7cm and one rectangle of dimensions 3cm x 1cm is cut. Find the total surface area of remaining box? ​

Answer 1

$\underline {\blue { Dimensions \: of \: a \: cuboidal \: box :}}$

$l \times b \times h = 21\:cm \times 14 \:cm \times 7 \:cm$

$\red { Total \: surface \:Area \: of \:the \:box }$

$= \pink { 2(lb + bh + lh) }$

$= 2( 21 \times14 + 14 \times 7 + 7 \times 21 )\\= 2( 294 + 98 + 147) \\= 2 \times 539 \\= 1078\: cm^{2} \: ---(1)$

$\underline {\blue { Dimensions \: of \: a \: circle :}}$

$Diameter (d) = 7 \:cm$

$\boxed { \orange { Area \: of \:a \:circle = \pi \frac{d^{2}}{4} }}$

$Area \: of \: 2 \: circles = 2 \times \pi \times \frac{7^{2}}{4} \\= 2 \times \frac{22}{7} \times \frac{7^{2}}{4} \\= 77 \:cm^{2} \: ---(2)$

$\underline {\blue { Dimensions \: of \: a \: rectangle:}}$

$Length = 3 \: cm , \: Breadth = 1 \:cm$

$\implies \red {Area \: of \: the \: rectangle }$

$= Length \times breadth \\= 3 \times 1 \\= 3 \:cm^{2} \: ---(3)$

$Now , \green {Total \: surface \: area \: of \: remaining \:box }$

$= T.S.A \: of \: the \: box \\-(Area \:of \:two \: circles ) \\- (area \: of \: the \: rectangle )$

$= 1078 \:cm^{2} - 77 \:cm^{2} - 3 \:cm^{2} \\= 998 \:cm^{2}$

Therefore.,

$\red {Total \: surface \: area \: of \: remaining \:box }$

$\green {= 998 \:cm^{2}}$

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