Question

A right rectangular prism measures 10 cm tall, 6 cm long, and 5 cm wide. A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled? Enter your answer, to the nearest tenth, in the box.

Answer 1

The surface area of a right rectangular prism is given by 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

We are given that the original prism has dimensions of 10 cm x 6 cm x 5 cm, so the surface area is 2(6)(5) + 2(10)(5) + 2(10)(6) = 120 cm^2.

To double this, we need the new surface area to be 2 * 120 cm^2 = 240 cm^2.

The formula of surface area is 2lw + 2lh + 2wh
So, we can say 2(6)(5) + 2(10)(5) + 2(10)(6) = 2lw + 2lh + 2wh =120cm^2

To double the surface area we need to make this equation equal to 240cm^2

So, 2lw + 2lh + 2wh =240cm^2

Now, we know the values of l,w,h for the original prism, we can use the same values to calculate the height of the new prism.

2(6)(5) + 2(10)(5) + 2(10)(6) = 240

We can solve for h, we get h = 15cm

So, to double the surface area, the height of the new prism should be 15cm.