PSLE A rectangular block M was cut along the dotted line into two smaller rectangular blocks of equal height, N and P, as shown. The volume of P is 14280 cm
3 more than that of N.
- What is the height of each block?
- Sean packed 6 of block P such that they fit exactly into a box with a square base. The box has the same height as P. At most, how many of block N can be packed into such a box?
(a)
Base area of Block N
= 12 x 28
= 336 cm
2 Base area of Block P
= 42 x 28
= 1176 cm
2 Base area of Block P more than Block N
= 1176 - 336
= 840 cm
2 Height of each block
= 14280 ÷ 840
= 17 cm
(b)
Base area of the box
= 6 x 1176
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block N along the length of the box
= 84 ÷ 12
= 7 r 0
Number of Block N along the breadth of the box
= 84 ÷ 28
= 3
Number of Block N to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 17 cm; (b) 21