The height of a cone, a cylinder and a sphere are equal numerically. If the ratio of their radii is 1:3:5, then find the ratio of their volumes? |
1:27:200 5:9:1 1:27:125 1:9:25 |
1:27:200 |
since in a sphere, height = diameter :- Cone Cylinder Sphere Ratio of radius 1 : 3 : 5 Ratio of height 1 : 1 : 1 ⇒ height of cone and cylinder = diameter of sphere Ratio of volume \(\frac{1}{3}\) \(\pi \)r12h1 : \(\pi \)r22h2 : \(\frac{4}{3}\) \(\pi \)r33 ⇒ \(\frac{1}{3}\) \(\pi \)x2 × \(\frac{5x}{2}\) : \(\pi \)(3x)2 \(\frac{5x}{2}\) : \(\frac{4}{3}\) \(\pi \) 5x)2 ⇒ \(\frac{5}{6}\) : \(\frac{9 × 5}{2}\) : \(\frac{4}{3}\) × 125 = 1 : 27 : 200 |