Question

$\bf{QueStioNS : }$

1. Find the volume and total surface area of a right circular solid cylinder whose radius and height are 14 cm and 20 cm, respectively.

2. In the attachment!!!

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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Radius of cylinder, r = 14 cm

• Height of cylinder, h = 20 cm

We know,

Volume of cylinder of radius r and height h is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ Volume_{(Cylinder)} = \pi \: {r}^{2} \: h \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Volume_{(Cylinder)} = \dfrac{22}{7} \times 14 \times 14 \times 20$

$\rm :\longmapsto\:Volume_{(Cylinder)} = 22 \times 2 \times 14 \times 20$

$\\ \purple{\rm\implies \boxed{\tt{ \:Volume_{(Cylinder)} = 12320 \: {cm}^{3}}}}$

Now,

We know Total Surface Area (TSA) of cylinder of radius r and height h is given by

$\red{\rm :\longmapsto\:\boxed{\tt{ \: TSA_{(Cylinder)} \: = \: 2\pi \: r(h + r) \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:TSA_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 14 \times (14 + 20)$

$\rm :\longmapsto\:TSA_{(Cylinder)} = 2 \times 22 \times 2 \times 34$

$\red{\rm\implies \:\boxed{\tt{ TSA_{(Cylinder)} = 2992 \: {cm}^{2} \: }}}$

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More information :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²