Question

Victor is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular prism. He now needs to cover the wooden blocks on all sides with a red fabric.

How much fabric does Victor need in order to cover 12 of these blocks?


156 cm²

24 cm²

13 cm²

2 cm²

Answer 1

156 cm² for K12

Answer 2

(a) 156 cm²

Explanation:

The total surface area of the 12 blocks can be computed by first finding the surface area of one block. That result can then be multiplied by 12. The area of one rectangular prism is given by the formula ...

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

A = 2(4·1 +1/2(4+1)) = 2(4 +5/2) = 13 . . . cm²

The area of 12 such prisms will be ...

12 × (13 cm²) = 156 cm²

Victor needs 156 cm² of fabric to cover 12 blocks.

_____

Additional comment

This problem offers an opportunity to exercise your number sense. The area of the largest surface of one block is (4 cm)×(1 cm) = 4 cm². 12 of these surfaces will have an area of 48 cm². This is only part of the total area, so the only reasonable choice among those offered is 156 cm².