PSLE A rectangular block B was cut along the dotted line into two smaller rectangular blocks of equal height, C and D, as shown. The volume of D is 24288 cm
3 more than that of C.
- What is the height of each block?
- Simon packed 6 of block D such that they fit exactly into a box with a square base. The box has the same height as D. At most, how many of block C can be packed into such a box?
(a)
Base area of Block C
= 15 x 32
= 480 cm
2 Base area of Block D
= 48 x 32
= 1536 cm
2 Base area of Block D more than Block C
= 1536 - 480
= 1056 cm
2 Height of each block
= 24288 ÷ 1056
= 23 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block C along the length of the box
= 96 ÷ 15
= 6 r 6
Number of Block C along the breadth of the box
= 96 ÷ 32
= 3
Number of Block C to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 23 cm; (b) 18