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 252 cm
3 more than that of U.
- What is the height of each block?
- Vaidev 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
= 3 x 6
= 18 cm
2 Base area of Block V
= 9 x 6
= 54 cm
2 Base area of Block V more than Block U
= 54 - 18
= 36 cm
2 Height of each block
= 252 ÷ 36
= 7 cm
(b)
Base area of the box
= 6 x 54
= 324 cm
3 Length of the box
= √324
= 18 cm
Number of Block U along the length of the box
= 18 ÷ 3
= 6 r 0
Number of Block U along the breadth of the box
= 18 ÷ 6
= 3
Number of Block U to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 7 cm; (b) 18