Volume and Surface Area Questions
Choose the correct option.
Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
Answer: Option D
Choose the correct option.
A sphere and a cube have the same surface area. Find the ratio of their volumes?
Answer: Option A
SA of a sphere: 4πrÂ²
SA of a cube: 6xÂ²
4πrÂ² = 6xÂ²
rÂ²/xÂ² = 6 / 4π
(r/x)Â² = 3 / 2π
r/x = (3 / 2π)^0.5
Volume of a sphere: 4/3 πrÂ³
Volume of a cube: xÂ³
Find the ratio meaning (4/3 πrÂ³)/xÂ³
= (4π/3)(3 / 2π)^1.5
= (2Â²π/3)[3^1.5 / (2^1.5)(π^1.5)]
= âˆš2âˆš3 / âˆšπ
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