The base radii of two cylinders are in the ratio 2:3 and their height

1.	The base radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.i. What is the ratio of their volumes?ii. The volume of the first cylinder is 720 cubic centimetres. What is the volume of the second?
Answer» i. If the base radius of the first cylinder is 2r then base radius of the second one is 3r. Height of the first cylinder is 5h and second cylinder is 4h. Volume of the first cylinder = Base area × height . = π × 2r × 2r × 5h = 20 π r²h. Volume of the second cylinder = π × 3r × 3r × 4h = 36 πr²h. The ratio between the volumes = 20πr² h : 36πr² h = 20 : 36.= 5 : 9 ii. The volume of the first cylinder is 720 cm³ is given. Let consider the volume of the second cylinder be x, then the ratio between the volumes is 5: 9 5 : 9 = 720 : x 5 × x = 9 × 720 x = 1296 Volume of the second cylinder = 1296 cm³

The base radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.i. What is the ratio of their volumes?ii. The volume of the first cylinder is 720 cubic centimetres. What is the volume of the second?

Answer»

i. If the base radius of the first cylinder is 2r then base radius of the second one is 3r. Height of the first cylinder is 5h and second cylinder is 4h.

Volume of the first cylinder

= Base area × height .

= π × 2r × 2r × 5h = 20 π r²h.

Volume of the second cylinder

= π × 3r × 3r × 4h = 36 πr²h.

The ratio between the volumes

= 20πr² h : 36πr² h = 20 : 36.= 5 : 9

ii. The volume of the first cylinder is 720 cm³ is given. Let consider the volume of the second cylinder be x, then the ratio between the volumes is 5: 9

5 : 9 = 720 : x

5 × x = 9 × 720

x = 1296

Volume of the second cylinder = 1296 cm³

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