Question

How many times do the volume and surface area of the cylinder increase if its radius doubled and height reamains same.

Answer 1

Answer:

v₂ = 4 v₁ , s₂ = 2 s₁

Step-by-step explanation:

Given--->

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Radius of cylinder is doubled and height of cylinder remains same

To find --->

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How many times do the volume and surface area of cylinder increases

Solution--->

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Case1--->

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Let radius and height of cylinder be r and h

Volume of cylindet( v₁ ) = π r² h

Surface area of cylinder ( s₁ ) = 2π r h

Case2--->

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Now radius of cylinder = 2r

height of cylinder = h

Volume of cylinder(v₂)= π (2r )² h

= π 4 r² h

= 4 (π r² h)

v₂ = 4 ( v₁ )

Surface area of cylinder = 2 π (2r ) h

s₂ = 2 ( 2π r h )

s₂ = 2 ( s₁ )

Answer 2

Answer:

Volume:-)

we know that volume of a cylinder is given by

$V = \pi {r}^{2} h$

When the radius is doubled i.e.

r' = 2r

volume will be

$V'= \pi {r'}^{2} h \\ \\ V' = \pi {(2r)}^{2} h = 4\pi {(r)}^{2}\\ \\V' =4V$

It give that when we double radius then the volume becomes four times.

Surface Area:-)

1) CSA:-

As CSA of a cylinder is given by

$CSA = 2 \pi rh$

when radius become doubled then CSA will be

$CSA' = 2 \pi r'h \\ \\ CSA' = 2 \pi2rh \\ \\ CSA' = 2 \times 2 \pi rh \\ \\ CSA' = 2CSA$

lt gives that when we double the radius then CSA will also be double.

TSA:-

TSA of any cylinder is given by

$TSA = 2 \pi r( h+ r)$

when radius is doubled TSA will be

$TSA'= 2 \pi r'(h + r') \\ \\ TSA' = 2 \pi2r(h + 2r) \\ \\ TSA =2 \times 2 \pi r(h + r + r) \\ \\ tsa = 4 \pi {r}^{2} + 2 \times 2 \pi r(h + r)$

it gives that when we double the radius then TSA will become

$twice + 4 \pi {r}^{2}\\ \\So, TSA'=2TSA+4 \pi {r}^{2}$