Question

11.

Paula designed a three-dimensional scale model of a department store. The volume of
the scale model was 35 cubic feet. The ratio of the dimensions of the model to the
dimensions of the store was 1:20. Determine the volume of the actual department
store that Paula planned to build.

Answer 1

Answer: The volume of the actual department store is 280,000 cubic feet

Step-by-step explanation: The question has provided the volume of the model built by Paula, and that is 35 cubic feet. The volume of a three sided solid is given as;

Volume = L x W x H

This can also be conveniently expressed as;

Volume = L³ (which implies that the solid has all sides measuring the same for simplicity's sake)

However, given that the ratio of the model to that of the actual store is 1:20, we simply use the given ratio to substitute for the value of the side of the actual store, hence we now have dimension as;

Volume = L³

35 = L³

Add the cube root to both sides of the equation

∛35 = L

The dimension of the actual store which is an enlargement by a ratio of 1:20 now becomes;

Actual store = 20 x L

Actual store = 20 x ∛35

Actual store = 20 x 3.27106631018859

Actual store = 65.42132620377179

Therefore the volume of the actual store is given as;

Volume = L³

Volume = 65.42132620377179³

Volume = 280000

Therefore the volume of the actual store is 280,000 cubic feet

Answer 2

V = 280000 cubic meters

Step-by-step explanation: Given that the volume of the scale model was 35 cubic feet. The ratio of the dimensions of the model to the

dimensions of the store was 1:20.

Let the volume of the actual department store that Paula planned to build be V. Then

35/V = (1/20)^3

35/V = 1/8000

Cross multiply

V = 8000 × 35

V = 280000 cubic meters