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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 $30$ 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? $\newline$ (Round to the nearest thousand cubic meters.)

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Understanding integers

Full solution

Q. 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?

\newline

(Round to the nearest thousand cubic meters.)

Calculate volume of original pond: Calculate the volume of the original cone-shaped pond. $\newline$ The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$ , where $r$ is the radius and $h$ is the height (or depth). $\newline$ We know: radius ( $r$ ) = $30$ meters, depth ( $h$ ) = $15$ meters, and $\pi \approx 3.14$ . $\newline$ Plug in the values to get the original volume: $V_{\text{original}} = \frac{1}{3}\pi(30)^2(15)$ .
Perform calculation for original volume: Perform the calculation for the original volume. $\newline$ $V_{\text{original}} = \frac{1}{3} \times 3.14 \times (30)^2 \times 15 = \frac{1}{3} \times 3.14 \times 900 \times 15$ $\newline$ $V_{\text{original}} = 3.14 \times 300 \times 15$ $\newline$ $V_{\text{original}} = 14130$ cubic meters
Calculate volume of enlarged pond: Calculate the volume of the enlarged cone-shaped pond. $\newline$ We know: new radius $r$ = $40$ meters, new depth $h$ = $20$ meters. $\newline$ Plug in the values to get the new volume: $V_{\text{new}} = \frac{1}{3}\pi(40)^2(20)$ .
Perform calculation for new volume: Perform the calculation for the new volume. $\newline$ $V_{\text{new}} = \frac{1}{3} \times 3.14 \times (40)^2 \times 20 = \frac{1}{3} \times 3.14 \times 1600 \times 20$ $\newline$ $V_{\text{new}} = 3.14 \times 533.3333 \times 20$ $\newline$ $V_{\text{new}} = 3.14 \times 10666.6667$ $\newline$ $V_{\text{new}} = 33493.3334$ cubic meters
Calculate difference in volume: Calculate the difference in volume to find out how much more water the pond will hold after the enlargement. $\newline$ Difference in volume = $V_{\text{new}} - V_{\text{original}}$ . $\newline$ Difference in volume = $33493.3334 - 14130$ . $\newline$ Difference in volume = $19363.3334$ cubic meters.
Convert difference in volume to thousands: Convert the difference in volume to thousands of cubic meters and round to the nearest thousand. $\newline$ Difference in volume (in thousands of cubic meters) = $\frac{19363.3334}{1000}$ $\newline$ Difference in volume (in thousands of cubic meters) $\approx 19.4$ $\newline$ Round to the nearest thousand: $\approx 19$ thousand cubic meters

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