Math, asked by ukarn56, 3 days ago

The base radius and the height of a cylinder are in the ratio 5:7.if the volume of the cylinder is 550 cubic cm, find the radius of the base of the cylinder.​

Answers

Answered by MяMαgıcıαη
66

Required Answer :-

Given :-

  • Ratio of base radius and height of a cylinder = 5:7
  • Volume of a cylinder = 550 cm³

To Find :-

  • Radius of the base of a cylinder?

Solution :-

Let base radius and height of a cylinder be 5y and 7y.

We know that formula of volume of cylinder is given by,

\star\:{\boxed{\sf{Volume_{(cylinder)} = \pi r^2h}}}

Putting all values,

\\ \longrightarrow\:\sf 550 = \dfrac{22}{\cancel{7}}\:\ast\:(5y)^2\:\ast\:\cancel{7}y

\\ \longrightarrow\:\sf 550 = 22\:\ast\:25y^2\:\ast\:y

\\ \longrightarrow\:\sf {\cancel{\dfrac{550}{22}}} = 25y^3

\\ \longrightarrow\:\sf 25 = 25y^3

\\ \longrightarrow\:\sf {\cancel{\dfrac{25}{25}}} = y^3

\\ \longrightarrow\:\sf 1 = y^3

\\ \longrightarrow\:\sf y^3 = 1

\\ \longrightarrow\:\sf y = \sqrt[3]{1}

\\ \longrightarrow\:\underline{\underline{\sf{y = 1}}}

Radius of base ::

  • r = 5y
  • r = 5 * 1
  • r = 5 cm

Henceforth, radius of base of a cylinder is 5 cm.

Important Formulae :-

↠ TSA of cube = 6a²

↠ CSA of cube = 4a²

↠ Volume of cube =

↠ TSA of cuboid = 2(lb + bh + hl)

↠ CSA of cuboid = 2(l + b)h

↠ Volume of cuboid = l × b × h

↠ TSA of cylinder = 2πr(r + h)

↠ CSA of cylinder = 2πrh

↠ Volume of cylinder = πr²h

↠ Volume of hollow cylinder = πh(R²-r²)

↠ TSA of cone = πr(l + r)

↠ CSA of cone = πrl

↠ Volume of cone = 1/3πr²h

↠ SA of sphere = 4πr²

↠ Volume of sphere = 4/3πr³

↠ TSA of hemisphere = 3πr²

↠ CSA of hemisphere = 2πr²

↠ Volume of hemisphere = 2/3πr³

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