Question

If the volume of a cone is 255 cubicm., what is the volume of a cylinder with same base radius and same height?

Answer 1

Solution

Given:-

• Volume of cone = 255 cm³
• Base, & Height of cone are same to cylinder .

Find:-

• Volume of cylinder .

Explanation

Important Formula

☛ Volume of cone = 1/3 .π.(r²).h

☛Volume of cylinder = π.r².h

A/C to question,

(Volume of cone = 255 cm³ )

➠ 255 = 1/3.(π.r².h)

➠ π.r².h = 255 × 3

➠ π.r².h = 765

But, condition A/c to question

Base & Height of cone are same to cylinder

So,

➠ Volume of cylinder = π.r².h

➠Volume of cylinder = 765 cm³

Hence

• Volume of cylinder = 765 cm³

_________________

Answer 2

$\huge{\underline{\underline{\mathrm{\blue{GIVEN:-}}}}}$

• The Volume of cone = 255 cm³
• The radius and height of the cone and cylinder are equal

$\huge{\underline{\underline{\mathrm{\blue{NEED\:TO\:FIND:-}}}}}$

Find the volume of cylinder = ?

$\huge{\underline{\underline{\mathrm{\blue{FORMULA\:USED:-}}}}}$

$\large{\boxed{\bf{\green{Volume \: of \:cone = \frac{1}{3}π{r}^{2}h}}}}$

$\large{\boxed{\bf{\green{Volume \:of\:Cylinder = π{r}^{2} h }}}}$

$\huge{\underline{\underline{\mathrm{\blue{SOLUTION:-}}}}}$

We have given that, the volume of cone is 255 cm³

∴ Putting the values in formula, we get

$\longrightarrow$ $\large\bf{Volume\: of\: cone = \frac{1}{3}π{r}^{2}h}$

$\longrightarrow$$\bf{255 = \frac{1}{3}π{r}^{2}h}$

$\longrightarrow$$\bf{ 255\times 3 = π{r}^{2} h}$

$\longrightarrow$$\large\bf\green{ 765 = π{r}^{2} h....1)}$

∴ Radius and height of cylinder are equal to the radius and height of cone

$\large\bf{Volume\:of\: cylinder = π {r}^{2} h}$

$\longrightarrow$$\bf\green{ π{r}^{2} h = 765 }$[from ...1)]

Hence, the volume of cylinder is 765 cm³

$\large{\underline{\underline{\mathrm{\blue{FINAL\:ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\mathrm{\green{Volume\:of \:Cylinder = 765\: {cm}^{3}}}}}}$