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 8778 cm
3 more than that of U.
- What is the height of each block?
- Tim packed 8 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
= 15 x 28
= 420 cm
2 Base area of Block V
= 42 x 28
= 882 cm
2 Base area of Block V more than Block U
= 882 - 420
= 462 cm
2 Height of each block
= 8778 ÷ 462
= 19 cm
(b)
Base area of the box
= 8 x 882
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block U along the length of the box
= 84 ÷ 15
= 5 r 9
Number of Block U along the breadth of the box
= 84 ÷ 28
= 3
Number of Block U to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 19 cm; (b) 15