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?

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.

Answer Link

23amazingallie 23amazingallie · Answer 2 · 2020-08-03T04:56:06-04:00

Answer:

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

Step-by-step 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.