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Julie is measuring two cones. Given the base radius r and height h of the first cone, Julie uses the formula V=(pir^(2)h)/(3) to compute its volume V to be 6 cubic meters. The second cone has the same height, but has 2 times the radius. What is its volume? Choose 1 answer: (A) 12 cubic meters (B) 4pi cubic meters (C) 24 cubic meters (D) 8pi cubic meters

Julie is measuring two cones.\newlineGiven the base radius r r and height h h of the first cone, Julie uses the formula\newlineV=πr2h3 V=\frac{\pi r^{2} h}{3} \newlineto compute its volume V V to be 66 cubic meters.\newlineThe second cone has the same height, but has 22 times the radius. What is its volume?\newlineChoose 11 answer:\newline(A) 1212 cubic meters\newline(B) 4π 4 \pi cubic meters\newline(C) 2424 cubic meters\newline(D) 8π 8 \pi cubic meters

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Q. Julie is measuring two cones.\newlineGiven the base radius r r and height h h of the first cone, Julie uses the formula\newlineV=πr2h3 V=\frac{\pi r^{2} h}{3} \newlineto compute its volume V V to be 66 cubic meters.\newlineThe second cone has the same height, but has 22 times the radius. What is its volume?\newlineChoose 11 answer:\newline(A) 1212 cubic meters\newline(B) 4π 4 \pi cubic meters\newline(C) 2424 cubic meters\newline(D) 8π 8 \pi cubic meters
  1. Understand Problem: Understand the problem and the given information.\newlineWe are given the volume of the first cone and the formula to calculate the volume of a cone. We are also told that the second cone has the same height as the first cone but twice the radius. We need to find the volume of the second cone.
  2. Express Radius and Height: Use the given volume of the first cone to express its radius and height in terms of the volume.\newlineThe volume of the first cone is given by the formula V=πr2h3V = \frac{\pi r^2 h}{3}, and we know that V=6V = 6 cubic meters. We can use this information to find the relationship between the radius and height for the first cone.
  3. Calculate Volume: Calculate the volume of the second cone using the relationship between the first cone's radius and height.\newlineSince the second cone has twice the radius of the first cone, if we let rr be the radius of the first cone, then the radius of the second cone is 2r2r. The volume of the second cone V2V_2 is given by V2=(π⋅(2r)2⋅h)/3V_2 = (\pi \cdot (2r)^2 \cdot h) / 3.
  4. Simplify Expression: Simplify the expression for the volume of the second cone.\newlineV2=π⋅(2r)2⋅h3=π⋅4r2⋅h3=4⋅π⋅r2⋅h3V_2 = \frac{\pi \cdot (2r)^2 \cdot h}{3} = \frac{\pi \cdot 4r^2 \cdot h}{3} = 4 \cdot \frac{\pi \cdot r^2 \cdot h}{3}\newlineSince we know the volume of the first cone is 66 cubic meters, we can substitute this value into our expression for V2V_2.\newlineV2=4⋅6=24V_2 = 4 \cdot 6 = 24 cubic meters
  5. Verify Calculation: Verify that the calculation is correct and does not contain any mathematical errors.\newlineWe have correctly applied the formula for the volume of a cone and accounted for the change in radius from the first cone to the second cone. The calculation appears to be free of mathematical errors.

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