Question

what is the ratio of cylinder and cone if the base and height remains same​

Answer 1

The ratio of the volume of cylinder to  the volume of cone = 1 : $\dfrac{1}{3}$ or, 3 : 1

Step-by-step explanation:

Let the radius of cylinder = The radius of cone = r and

The height of cylinder = The height of cone = h

To find, the ratio of the volume of cylinder to  the volume of cone = ?

We know that,

The volume of cylinder = $\pi r^2h$

and

The volume of cone = $\dfrac{1}{3} \pi r^2h$

∴ The ratio of the volume of cylinder to  the volume of cone

= $\pi r^2h$ : $\dfrac{1}{3} \pi r^2h$

= 1 : $\dfrac{1}{3}$

Multiplying by 3, we get

= 3 × 1 : $3\times \dfrac{1}{3}$

= 3 : 1

∴ The ratio of the volume of cylinder to  the volume of cone

= 1 : $\dfrac{1}{3}$ or, 3 : 1

Answer 2

Volume Ratio 3 : 1  ,

Step-by-step explanation:

ratio of cylinder and cone if the base and height remains same​

Let say radius of cone & cylinder = r

Height of cylinder & cone = h

Volume of Cylinder = π r²h

Volume of Cone = (1/3) π r²h

Ratio of Volume of Cylinder  to Volume of Cone = π r²h /  (1/3) π r²h

= 3 : 1

CSA of Cylinder = 2π r h

CSA of Cone = π r l  = π r√r² + h²

Ratio of CSA of Cylinder  to CSA of Cone = 2π r h  /  π r√r² + h²

= 2h/√r² + h²

TSA of Cylinder = 2π r h  + 2π r² =  2π r (r + h)

TSA of Cone = π r² + π r l  = π r(r + √r² + h²)

Ratio of CSA of Cylinder  to CSA of Cone = 2π r (r + h)  /  π r(r + √r² + h²)

= 2(r + h)/(r + √r² + h²)

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