Math, asked by nikhilgour1006, 1 year ago

the ratio between the curved surface area and total surface area and total surface area of a right circular cylinder 2:3 find the ratio between the radius and height of the cylinder​

Answers

Answered by Anonymous
1

Answer:

  • Ratio between he radius and height of the cylinder​ is 1:2.

Step-by-step explanation:

Given:

  • Ratio between CSA & TSA of cylinder = 2:3

To Find:

  • Ratio between height and radius.

Let the radius and height of the cylinder be r and h.

We know that,

⇒ Curved surface area of cylinder = 2πrh

⇒ Total surface area of cylinder = 2πr(r + h)

\tt{\implies \dfrac{2\pi rh}{2\pi r(r+h)}=\dfrac{2}{3}}

\tt{\implies \dfrac{h}{r+h}=\dfrac{2}{3}}

\tt{\implies 2r+2h=3h}

\tt{\implies 2r=3h-2h}

\tt{\implies 2r=h}

\tt{\implies r:h=1:2}

Hence, ratio between he radius and height of the cylinder​ is 1:2.

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Answered by Anonymous
9

\huge\underline\mathrm{SOLUTION:-}

AnswEr:

  • Ratio of height to radius = 2:1.

Given:

  • The ratio between the curved surface area and total surface area and total surface area of a right circular cylinder 2:3.

Need To Find:

  • The ratio between the radius and height of the cylinder = ?

ExPlanation:

Let the height and radius of the right circular cylinder be h and r respectively.

  • Curved surface area of right cicular cylinder = 2πrh

Total surface area of right circular cylinder = 2πrh + 2πr2 = 2πr(h + r)

So, ratio of curved surface area to total surface area = \mathsf {\frac{2\pi rh}{2\pi r(h + r)} }

\mathsf {\frac{h}{h + r} = \frac{2}{3} }

\mathsf {3h = 2h\:+\: 2r}

\mathsf {h = 2r}

\mathsf {\frac{h}{r} = \frac{1}{2} }

  • So, ratio of height to radius is 2:1.

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