Questions: If a spherical tank 4 m in diameter can be filled with a liquid for 700, find the cost to fill a tank 16 m in diameter. The cost to fill the 16 m tank is

If a spherical tank 4 m in diameter can be filled with a liquid for 700, find the cost to fill a tank 16 m in diameter. The cost to fill the 16 m tank is
Transcript text: If a spherical tank 4 m in diameter can be filled with a liquid for $\$ 700$, find the cost to fill a tank 16 m in diameter. The cost to fill the 16 m tank is \$ $\square$
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Solution

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Solution Steps

Step 1: Calculate the volume of the first spherical tank

Using the formula $V_1 = \frac43\pi(\frac{D_1}{2})^3$, where $D_1 = 4$, we find $V_1 = 33.510$ cubic units.

Step 2: Calculate the volume of the second spherical tank

Using the formula $V_2 = \frac43\pi(\frac{D_2}{2})^3$, where $D_2 = 16$, we find $V_2 = 2144.661$ cubic units.

Step 3: Determine the ratio of the volumes

The ratio $R = \frac{V_2}{V_1} = 64$, indicating how many times larger the second tank is compared to the first.

Step 4: Calculate the cost to fill the second tank

Given the cost to fill the first tank is $700$, the cost to fill the second tank is $C_2 = C_1 \times R = 44800$.

Final Answer:

The cost to fill the spherical tank of diameter 16 is approximately $44800.

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