PSLE A rectangular block V was cut along the dotted line into two smaller rectangular blocks of equal height, W and X, as shown. The volume of X is 11520 cm
3 more than that of W.
- What is the height of each block?
- Henry packed 8 of block X such that they fit exactly into a box with a square base. The box has the same height as X. At most, how many of block W can be packed into such a box?
(a)
Base area of Block W
= 21 x 32
= 672 cm
2 Base area of Block X
= 48 x 32
= 1152 cm
2 Base area of Block X more than Block W
= 1152 - 672
= 480 cm
2 Height of each block
= 11520 ÷ 480
= 24 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block W along the length of the box
= 96 ÷ 21
= 4 r 12
Number of Block W along the breadth of the box
= 96 ÷ 32
= 3
Number of Block W to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 24 cm; (b) 12