Multiple choice

The base and top radius of a truncated cone is 1.5 m and 2 m respectively. The height of the cone is 60 m. What is the volume of a truncated cone? (Use $\pi$ = 3).

  1. 555 m$^3$
  2. 545 m$^3$
  3. 535 m$^3$
  4. 525 m$^3$
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A Correct answer
Explanation

Volume of truncated cone = (1/3) * pi * h * (r1^2 + r2^2 + r1*r2). Given r1=1.5, r2=2, h=60, pi=3. Volume = (1/3) * 3 * 60 * (1.5^2 + 2^2 + 1.5*2) = 60 * (2.25 + 4 + 3) = 60 * 9.25 = 555.

AI explanation

Using the frustum volume formula V = (1/3) pi h (R squared + Rr + r squared) with R = 2, r = 1.5, h = 60, and pi = 3, calculate the sum inside the parentheses as 2 squared + 2 times 1.5 + 1.5 squared, which equals 9.25. The volume is then (1/3) times 3 times 60 times 9.25, resulting in 555 cubic m.

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