Question

The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up?

Answer 1

The mock-up is 216 times smaller than the actual tank size.

Explanation:

To find how many times smaller the mock-up tank is from the actual main show tank, we first need to find the volume of the mock-up tank. Since each dimension is made 6 times smaller, the radius, 70, needs to be divided by 6 which equals 11.67. In addition, because we are calculating for a quarter-sphere sized tank we need to divide the sphere formula by 4, turning
`V= 4/3(\pi * r^3)\\` into
`V= 1/3 (\pi * r^3)`. We can then create the equation:
`V= 1/3 (3.14 * 11.67^3)`. Once solved,
`V= 1663.492938` which equals, rounded to the nearest whole number, 216. Therefore, the mock-up tank is 216 times smaller than the actual tank.

Answer 2

Tank calculations :
Volume = 1/4(4/3 * pi * r^3)
r= 70 feet.
Volume = 1/4(4/3 * 3.14 * 70^3)
Calculating the values:
Volume = 359,000.67 ft.cubed

No we divide the actual radius by 6 to get the volume of scale model.
Hence,
6^3 = 216 times smaller.