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 14352 cm
3 more than that of U.
- What is the height of each block?
- Valen 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
= 15 x 26
= 390 cm
2 Base area of Block V
= 39 x 26
= 1014 cm
2 Base area of Block V more than Block U
= 1014 - 390
= 624 cm
2 Height of each block
= 14352 ÷ 624
= 23 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block U along the length of the box
= 78 ÷ 15
= 5 r 3
Number of Block U along the breadth of the box
= 78 ÷ 26
= 3
Number of Block U to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 23 cm; (b) 15