Question

find the diameter of a cylinder whose hieght is 5cm and numerical value is volume is equal to numarical value of curved surface area​

Answer 1

Question :

find the diameter of a cylinder whose height is 5cm and numerical value is volume is equal to numerical value of curved surface area .

Answer :

$\sf\pink{Given:}$

• height of a cylinder is 5 cm .

• numerical value of volume of the cylinder is equal to the numerical value of curved surface area of that cylinder .

$\sf\pink{To\:find:}$

• The diameter of the cylinder ?

Explanation :

let's find out the volume of the cylinder with the height 5 cm .

We know that ,

$\sf\purple{ volume\:of\:cylinder = \pi {r}^{2} h }$

• putting the value of h as 5.

$\\ \longrightarrow\sf{ \pi {r}^{2} 5}$

• Therefore the volume of the cylinder is πr²5 cm .

let's find out the curved surface area of cylinder with the height 5 cm .

$\sf\purple{ C.S.A\:of\:cylinder = 2\pi rh }$

• putting value of h as 5

$\\ \longrightarrow\sf{2\pi r5}$

Therefore the curved surface area of the cylinder is 2πr5 .

Equation Formed :

πr²5 = 2πr5

Reason :

volume of cylinder = curved surface area .

$\\ \longrightarrow\sf{ \pi {r}^{2}5 = 2\pi r5}$

• cancelling same terms on both sides .

$\\ \longrightarrow\sf{ r = 2}$

• Therefore we get the value of "r" that is the radius as 2 .

$\sf\purple{ Diameter = 2\times radius }$

$\\ \longrightarrow\sf{ 2\times 2}$

$\\ \longrightarrow\sf{4}$

• Therefore the diameter is 4 cm

please mark as brainliest .

Answer 2

find the diameter of a cylinder whose height is 5cm and numerical value is volume is equal to numerical value of curved surface area .

Answer :

\sf\pink{Given:}Given:

height of a cylinder is 5 cm .

numerical value of volume of the cylinder is equal to the numerical value of curved surface area of that cylinder .

\sf\pink{To\:find:}Tofind:

The diameter of the cylinder ?

Explanation :

let's find out the volume of the cylinder with the height 5 cm .

We know that ,

\sf\purple{ volume\:of\:cylinder = \pi {r}^{2} h }volumeofcylinder=πr

2

h

putting the value of h as 5.

\begin{gathered}\\ \longrightarrow\sf{ \pi {r}^{2} 5}\end{gathered}

⟶πr

2

5

Therefore the volume of the cylinder is πr²5 cm .

let's find out the curved surface area of cylinder with the height 5 cm .

\sf\purple{ C.S.A\:of\:cylinder = 2\pi rh }C.S.Aofcylinder=2πrh

putting value of h as 5

\begin{gathered}\\ \longrightarrow\sf{2\pi r5}\end{gathered}

⟶2πr5

Therefore the curved surface area of the cylinder is 2πr5 .

Equation Formed :

πr²5 = 2πr5

Reason :

volume of cylinder = curved surface area .

\begin{gathered}\\ \longrightarrow\sf{ \pi {r}^{2}5 = 2\pi r5}\end{gathered}

⟶πr

2

5=2πr5

cancelling same terms on both sides .

\begin{gathered}\\ \longrightarrow\sf{ r = 2}\end{gathered}

⟶r=2

Therefore we get the value of "r" that is the radius as 2 .

\sf\purple{ Diameter = 2\times radius }Diameter=2×radius

\begin{gathered}\\ \longrightarrow\sf{ 2\times 2}\end{gathered}

⟶2×2

\begin{gathered}\\ \longrightarrow\sf{4}\end{gathered}

⟶4

Therefore the diameter is 4 cm

please mark as brainliest