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A triangle with sides 3 cm, 4 cm and 5 cm is rotated with 3 cm and 4 cm sides as the heights one by one to form 2 different cones. The volumes of the cones so formed will be in the ratio of:
4:3
3:4
27:64
64:27
- A triangle with sides 3 cm, 4 cm, and 5 cm is a right-angled triangle.
- To form a cone, we rotate the triangle around one of its perpendicular (height) sides.
- Cone 1 is formed by rotating around the 3 cm side. The 3 cm becomes the height (h), and the 4 cm side is the base radius (r).
- Volume \( V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (4)^2 (3) = 16\pi \).
- Cone 2 is formed by rotating around the 4 cm side. The 4 cm becomes the height (h), and the 3 cm side is the base radius (r).
- Volume \( V_2 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3)^2 (4) = 12\pi \).
- The volume ratio \( V_1:V_2 = 16\pi : 12 \pi = 4:3 \).
- Answer: Option 1 - 4:3
- “”
By: Parvesh Mehta ProfileResourcesReport error
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