Question

15. Find the curved surface area, the total surface area and the volume of a cylinder, the
diameter of whose base is 7 cm and height being 60 cm. Also, find the capacity of the
cylinder in litres

​

Answer 1

Given:-

• Diameter= 7cm
• Height = 60cm

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To find:-

• Curved surface area of cylinder.
• Total surface area of cylinder.
• Volume of cylinder.

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For curved surface area of cylinder:-

Radius = $\sf \dfrac{diameter}{2} =\sf \dfrac{7}{2}$

Height = 60cm

According to the following formula:-

$\large {\boxed {\boxed {\red {\sf {Curved\: surface\: area { 2\pi rh} }}}}}$

Now, putting values we will get:-

$\implies \sf C.S.A = 2\pi r h \\ \\ \implies \sf 2 \times \dfrac{22}{7} \times \dfrac{7}{2} \times 60 \\ \\ \sf = 1320cm^{2}$

For total surface area of cylinder :-

From above we know that radius =$\dfrac{7}{2}$

Height=60cm

According to the following formula:-

$\large {\boxed {\boxed {\red {\sf {Total \: surface \: area = 2\pi \: r(r + h) }}}}}$

Putting the value we will get:-

$\implies \sf T.S.A = 2\pi \: r(r + h) \\ \\ \implies \sf 2 \times \dfrac{22}{7} \times \dfrac{7}{2} \bigg(\dfrac{7}{2} + 60\bigg) \\ \\ \implies \sf 22 \bigg(\dfrac{127}{2}\bigg) \\ \\ \implies \sf = 11 \times 127 \\ \\ \implies \sf = 1397cm^{2}$

For volume of cylinder:-

$\sf radius = \dfrac{7}{2}$

Height = 60cm

According to the following formula:-

$\large {\boxed {\boxed {\red {\sf {Volume = \pi \times r^{2} \times h}}}}}$

Putting the values we will get:-

$\implies \sf Volume \: of \: cylinder= \pi \times r^{2} \times h \\ \\ \implies \sf \bigg(\dfrac{22}{7} \times 3.5 \times 3.5 \times 60 \bigg) cm^{3} \\ \\ \implies \sf = 2310cm^{3}$

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Capacity in litres:-

$\implies \sf 1 \:litre = 1000cm^{3} \\ \\ \implies \sf 1cm^{3} = \dfrac{1}{1000} litre \\ \\ \implies \sf 2310cm^{3} = \dfrac{2310}{1000} litre \\ \\ \implies \sf = 2.31litre$

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So,

curved surface area = 1320cm²

total surface area = 1397cm²

volume= 2310cm³

Capacity of cylinder in litres = 2.31litre

Some formulas to know:-

$\implies \sf Total \: surface \: area \: of \: cuboid = 2(lh + bh + lb) \\ \\ \implies \sf Total \: surface \: area \: of \: cube = 6a^{2} \\ \\ \implies \sf Total \: surface \: area \: of \: cylinder = 2\pi \: r(h + r) \\ \\ \implies \sf Total \: surface \: area\: of \: cone = \pi \: r(l + r) \\ \\ \implies \sf Total \: surface \: area \: of \: Sphere= 4\pi \: r^{2} \\ \\ \implies \sf Total \: surface \: area\: of \: hemisphere= 3\pi \: r^{3}$

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$\implies \sf Curved\: surface\: area\: of\: cuboid= 2h(l + b) \\ \\ \implies \sf Curved \: surface\: area\: of \: cube = 4a^{2} \\ \\ \implies \sf Curved \: surface\: area\:of \: cylinder = 2\pi \: r \: h \\ \\ \implies \sf Curved \: surface\: area\: of\: cone = \pi \: r \: l \\ \\ \implies \sf Curved\: surface\: area\: of\: sphere= 4\pi \: r^{2} \\ \\ \implies \sf Curved \: surface\: area\: of \: hemisphere= 2\pi \: r^{2}$

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$\implies \sf Volume \: of \: cuboid= l \times b \times h \\ \\ \implies \sf Volume \: of \:cube = a^{3} \\ \\ \implies \sf Volume \: of \: cylinder = \pi \: r^{2}h \\ \\ \implies \sf Volume \: of \: cone = \dfrac{1}{3} \pi \: r^{2}h \\ \\ \implies \sf Volume \: of \: Sphere = \dfrac{4}{3} \pi \: r^{3} \\ \\ \implies \sf Volume \: of \: hemisphere= \dfrac{2}{3} \pi \:r^{3}$