Cole has a rectangular prism that measures 4in by 5 inches by 6 inches. He says by changing 1 dimension he can make a prism of 240 inches. What are the 3 ways he can do this?

First way: change in the 4 in dimension to 8 in

Second way: change in the 5 in dimension to 10 in

Third way: change in the 6 in dimension to 12 in

Step-by-step explanation:

The volume of a rectangular prism can be calculated by multiplying all the 3 dimensions:

Volume = 4 * 5 * 6 = 120 in3

To make a prism of 240 inches changing 1 dimension, Cole can choose any of the three dimensions to change.

First way: change in the 4 inches dimension:

Volume = x * 5 * 6 = 240

x = 8 inches

Second way: change in the 5 inches dimension:

Volume = 4 * x * 6 = 240

x = 10 inches

Third way: change in the 6 inches dimension:

Volume = 4 * 5 * x = 240

x = 12 inches

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: