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

22.7 cm

Explanation:

You want the height of a prism that has double the surface area of one that is 10 cm high with a base that is 6 cm by 5 cm.

Area

The area of a rectangular prism is given by ...

A = 2(LW +H(L +W))

For the given dimensions, this is ...

A = 2(6·5 +10(6 +5)) = 2(30 +10(11)) = 2(140) = 280 . . . . square cm

Double this area is 2×280 = 560 square cm.

New height

For the total area to be 560 cm², the height will be ...

560 = 2(30 +h(11)) . . . . . . filling in values we know

280 = 30 +11h . . . . . . . . divide by 2

250 = 11h . . . . . . . . . . . subtract 30

250/11 = h = 22 8/11 ≈ 22.7 . . . . cm

The height of the new prism should be 22.7 cm.

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