Question

Simple Question!!

If the height of the cylinder is equal to its diameter and the volume is 58212 cm³, then find the CSA and TSA of the cylinder.​

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Answer 1

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

Given that,

The height of the cylinder is equal to its diameter.

Let assume that

• Radius of cylinder be r cm

So,

• Diameter of cylinder = 2r cm

Thus,

• Height of cylinder, h = 2r cm

Also, given that,

• The volume of cylinder is 58212 cm³

We know

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Volume_{cylinder} = \pi \: {r}^{2}h \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:58212 = \dfrac{22}{7} \times {r}^{2} \times 2r$

$\rm :\longmapsto\:58212 = \dfrac{44}{7} \times {r}^{3}$

$\rm :\longmapsto\:1323 = \dfrac{1}{7} \times {r}^{3}$

$\rm :\longmapsto\: {r}^{3} = 7 \times 7 \times 7 \times 3 \times 3 \times 3$

$\rm :\longmapsto\: {r}^{3} = {(7 \times 3)}^{3}$

$\rm \implies\:\boxed{ \tt{ \: r \: = \: 21 \: cm \: }}$

So, we get

Radius of cylinder, r = 21 cm

Height of cylinder, h = 2r = 2 × 21 = 42 cm

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: CSA_{cylinder} = 2\pi \: rh}}}$

So, on substituting the values, we get

$\rm :\longmapsto\:CSA_{cylinder} = 2 \times \dfrac{22}{7} \times 21 \times 42$

$\rm :\longmapsto\:CSA_{cylinder} = 2 \times 22 \times 3 \times 42$

$\rm \implies\:\boxed{ \tt{ \: CSA_{cylinder} = 5544 \: {cm}^{2} \: }}$

Also, We know that

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

So, on substituting the values, we get

$\rm :\longmapsto\:TSA_{cylinder} = 2 \times \dfrac{22}{7} \times 21 \times (21 + 42)$

$\rm :\longmapsto\:TSA_{cylinder} = 2 \times 22 \times 3 \times 63$

$\rm \implies\:\boxed{ \tt{ \: TSA_{cylinder} = 8316 \: {cm}^{2} \: }}$

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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