Question

The radii of two cylinders are in the ratio 1:2 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The ratio of their volumes is 5:12 and the ratio of their curved surfaces is 5:6

Step-by-step explanation:

The radii of two cylinders are in the ratio 1:2

Let the ratio be x

So, Radius of cylinder 1 = x

Radius of cylinder 2 = 2x

Their heights are in the ratio 5:3.

Let the ratio be y

So, Height of cylinder 1 = 5y

Height of cylinder 2 = 3y

Volume of cylinder 1 =$\pi r^2 h = \pi (x)^2(5y)$

Volume of cylinder 2 = $\pi r^2 h = \pi (2x)^2(3y)$

Ratio of volumes = $\frac{ \pi (x)^2(5y)}{ \pi (2x)^2(3y)}=\frac{5}{12}$

Curved surface area of cylinder 1 = $2 \pi rh = 2 \pi (x)(5y)$

Curved surface area of cylinder 2 =$2 \pi rh = 2 \pi (2x)(3y)$

Ratio of curved surfaces = $\frac{2 \pi (x)(5y)}{2 \pi (2x)(3y)}=\frac{5}{6}$

Hence the ratio of their volumes is 5:12 and the ratio of their curved surfaces is 5:6

#Learn more:

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3 calculate the ratio of their volumes and the ratio of their curved surfaces

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