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What is the ratio of the radii of a cone and a cylinder if they have the same volume and height?
Wiki User
∙ 6y ago
Let the cylinder have radius R and height h
Let the cone have radius r and same height h
Then:
Volume cylinder = πr²h
Volume cone = ⅓πR²h
If the volume are equal:
⅓πR²h = πr²h
→ ⅓R² = r²
→ R² = 3r²
→ R = √3 r
→ ratio radii cone : cylinder = 1 : √3
Wiki User
∙ 6y ago
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The radii of two circular cylinders are in the ratio 2 3 and their height are in ratio 5 4 calculate the ratio of their volumes?
Let the radius of the first be 2r; then the radius of the second is 3r Let the height of the first be 5h; then the height of the second is 4h volume cylinder = π × radius² × height → volume first = π × (2r)² × 5h = 20πr²h → volume second = π × (3r)² × 4h = 36πr²h → ratio of their volumes is: 20πr²h : 36πr²h = 20 : 36 (divide by πr²h) = 5 : 9 (divide by 4)
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The radii of two circular cylinders are in the ratio 2 3 and their height are in ratio 5 4 calculate the ratio of their volumes?
Let the radius of the first be 2r; then the radius of the second is 3r Let the height of the first be 5h; then the height of the second is 4h volume cylinder = π × radius² × height → volume first = π × (2r)² × 5h = 20πr²h → volume second = π × (3r)² × 4h = 36πr²h → ratio of their volumes is: 20πr²h : 36πr²h = 20 : 36 (divide by πr²h) = 5 : 9 (divide by 4)
Calculate surface area to volume ratio cylinder?
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What is the ratio for the volumes of two similar spheres given that the ratio of their radii is 3 4?
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