PSLE A rectangular block U was cut along the dotted line into two smaller rectangular blocks of equal height, V and W, as shown. The volume of W is 726 cm
3 more than that of V.
- What is the height of each block?
- Sean packed 8 of block W such that they fit exactly into a box with a square base. The box has the same height as W. At most, how many of block V can be packed into such a box?
(a)
Base area of Block V
= 8 x 12
= 96 cm
2 Base area of Block W
= 18 x 12
= 162 cm
2 Base area of Block W more than Block V
= 162 - 96
= 66 cm
2 Height of each block
= 726 ÷ 66
= 11 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block V along the length of the box
= 36 ÷ 8
= 4 r 4
Number of Block V along the breadth of the box
= 36 ÷ 12
= 3
Number of Block V to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 11 cm; (b) 12