PSLE A rectangular block T was cut along the dotted line into two smaller rectangular blocks of equal height, U and V, as shown. The volume of V is 21824 cm
3 more than that of U.
- What is the height of each block?
- Charlie packed 6 of block V such that they fit exactly into a box with a square base. The box has the same height as V. At most, how many of block U can be packed into such a box?
(a)
Base area of Block U
= 17 x 32
= 544 cm
2 Base area of Block V
= 48 x 32
= 1536 cm
2 Base area of Block V more than Block U
= 1536 - 544
= 992 cm
2 Height of each block
= 21824 ÷ 992
= 22 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block U along the length of the box
= 96 ÷ 17
= 5 r 11
Number of Block U along the breadth of the box
= 96 ÷ 32
= 3
Number of Block U to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 22 cm; (b) 15