Question

as the set designer for his school's fall play, kenji is making a treasure chest shaped like a rectangular prism. the chest needs to hold approximately 6 cubic feet, or 10,368 cubic inches, of sand that will be spilled out during the first act. also, since an actor will stand on the chest in the second act, the chest needs to be 24 inches tall. kenji decides that the chest will be twice as long as it is wide. to the nearest tenth of an inch, what is the width of the chest?

Answer 1

To find the width of the treasure chest, we set up an equation using the given information. Solving the equation, we find that the width is approximately 14.7 inches.

Step-by-step explanation:

To find the width of the chest, we need to set up an equation using the given information. Let's assign the width as 'w' inches. According to the problem, the length of the chest is twice the width, so the length is '2w' inches. The height is given as 24 inches.

The volume of a rectangular prism can be found by multiplying the length, width, and height. We can set up the equation as:

(2w) * w * 24 = 10368

Simplifying the equation, we get:

48w^2 = 10368

Dividing both sides by 48, we get:

w^2 = 216

Taking the square root of both sides, we get:

w = 14.7

Therefore, the width of the chest is approximately 14.7 inches.

Answer 2

To find the width of the treasure chest in inches, set up an equation based on the given information and solve for 'w'. The approximate width of the chest is 9.1 inches.

Step-by-step explanation:

To find the width of the treasure chest, we can start by setting up equations based on the given information. Let's call the width of the chest 'w'. Since the chest is twice as long as it is wide, the length would be 2w. The height is given as 24 inches.

The volume of a rectangular prism is calculated by multiplying the length, width, and height. So we can set up the equation: 2w * w * 24 = 10,368 cubic inches.

Simplifying the equation, we get: 48w² = 10,368.

To solve for 'w', divide both sides of the equation by 48 and then take the square root. The approximate value of 'w' to the nearest tenth of an inch is 9.1 inches.