Two similar cylindrical cans have heights of 7cm and 21cm, if the smaller holds 250g of sugar, how many kg of sugar will the larger one hold?
A
0.75
B
1.5
C
2.25
D
3.5
E
6.75
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
- If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.
Given: Heights of cylinder --> 21 : 7 or 3 : 1 = \(\frac{3}{1}\)
= 3 times height enlargement
Volume / Capacity of larger cylinder = 3\(^3\) \(\times\) 250g
= 27 \(\times\) 250g = 6,750 or 6.75kg
Source: Myschool Past Questions Archive (Record #42251)