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 19040 cm
3 more than that of U.
- What is the height of each block?
- Lee 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
= 13 x 32
= 416 cm
2 Base area of Block V
= 48 x 32
= 1536 cm
2 Base area of Block V more than Block U
= 1536 - 416
= 1120 cm
2 Height of each block
= 19040 ÷ 1120
= 17 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 ÷ 13
= 7 r 5
Number of Block U along the breadth of the box
= 96 ÷ 32
= 3
Number of Block U to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 17 cm; (b) 21