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Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of 30 meters and a depth of 15 meters. He wants to increase the radius to 40 meters and the depth to 20 meters. How much more water will the pond hold, in thousands of cubic meters? (Round to the nearest thousand cubic meters.)

Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of 3030 meters and a depth of 1515 meters. He wants to increase the radius to 4040 meters and the depth to 2020 meters. How much more water will the pond hold, in thousands of cubic meters?\newline(Round to the nearest thousand cubic meters.)

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Q. Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of 3030 meters and a depth of 1515 meters. He wants to increase the radius to 4040 meters and the depth to 2020 meters. How much more water will the pond hold, in thousands of cubic meters?\newline(Round to the nearest thousand cubic meters.)
  1. Calculate volume of original pond: Calculate the volume of the original cone-shaped pond.\newlineThe formula for the volume of a cone is V=13πr2hV = \frac{1}{3}\pi r^2 h, where rr is the radius and hh is the height (or depth).\newlineWe know: radius (rr) = 3030 meters, depth (hh) = 1515 meters, and π≈3.14\pi \approx 3.14.\newlinePlug in the values to get the original volume: Voriginal=13π(30)2(15)V_{\text{original}} = \frac{1}{3}\pi(30)^2(15).
  2. Perform calculation for original volume: Perform the calculation for the original volume. \newlineVoriginal=13×3.14×(30)2×15=13×3.14×900×15V_{\text{original}} = \frac{1}{3} \times 3.14 \times (30)^2 \times 15 = \frac{1}{3} \times 3.14 \times 900 \times 15\newlineVoriginal=3.14×300×15V_{\text{original}} = 3.14 \times 300 \times 15\newlineVoriginal=14130V_{\text{original}} = 14130 cubic meters
  3. Calculate volume of enlarged pond: Calculate the volume of the enlarged cone-shaped pond.\newlineWe know: new radius rr = 4040 meters, new depth hh = 2020 meters.\newlinePlug in the values to get the new volume: Vnew=13π(40)2(20)V_{\text{new}} = \frac{1}{3}\pi(40)^2(20).
  4. Perform calculation for new volume: Perform the calculation for the new volume. \newlineVnew=13×3.14×(40)2×20=13×3.14×1600×20V_{\text{new}} = \frac{1}{3} \times 3.14 \times (40)^2 \times 20 = \frac{1}{3} \times 3.14 \times 1600 \times 20 \newlineVnew=3.14×533.3333×20V_{\text{new}} = 3.14 \times 533.3333 \times 20 \newlineVnew=3.14×10666.6667V_{\text{new}} = 3.14 \times 10666.6667 \newlineVnew=33493.3334V_{\text{new}} = 33493.3334 cubic meters
  5. Calculate difference in volume: Calculate the difference in volume to find out how much more water the pond will hold after the enlargement.\newlineDifference in volume = Vnew−VoriginalV_{\text{new}} - V_{\text{original}}.\newlineDifference in volume = 33493.3334−1413033493.3334 - 14130.\newlineDifference in volume = 19363.333419363.3334 cubic meters.
  6. Convert difference in volume to thousands: Convert the difference in volume to thousands of cubic meters and round to the nearest thousand.\newlineDifference in volume (in thousands of cubic meters) = 19363.33341000\frac{19363.3334}{1000}\newlineDifference in volume (in thousands of cubic meters) ≈19.4\approx 19.4\newlineRound to the nearest thousand: ≈19\approx 19 thousand cubic meters

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