PSLE A rectangular block P was cut along the dotted line into two smaller rectangular blocks of equal height, Q and R, as shown. The volume of R is 15200 cm
3 more than that of Q.
- What is the height of each block?
- Valen packed 8 of block R such that they fit exactly into a box with a square base. The box has the same height as R. At most, how many of block Q can be packed into such a box?
(a)
Base area of Block Q
= 17 x 32
= 544 cm
2 Base area of Block R
= 48 x 32
= 1152 cm
2 Base area of Block R more than Block Q
= 1152 - 544
= 608 cm
2 Height of each block
= 15200 ÷ 608
= 25 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block Q along the length of the box
= 96 ÷ 17
= 5 r 11
Number of Block Q along the breadth of the box
= 96 ÷ 32
= 3
Number of Block Q to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 25 cm; (b) 15