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 8694 cm
3 more than that of U.
- What is the height of each block?
- Henry 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
= 20 x 28
= 560 cm
2 Base area of Block V
= 42 x 28
= 882 cm
2 Base area of Block V more than Block U
= 882 - 560
= 322 cm
2 Height of each block
= 8694 ÷ 322
= 27 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 ÷ 20
= 4 r 4
Number of Block U along the breadth of the box
= 84 ÷ 28
= 3
Number of Block U to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 27 cm; (b) 12