The ratio of two similar prisms is 2:5 the volume of the larger is 375cm3 if sand is being poured into the smaller prism at 3cm3 per second how many seconds will it tAke to fill the smaller prism?
2/5 = x/375
5x = 750
x = 150
150/3 = 50 seconds
Find the volume of the smaller one by using a proportion. The volume is 150, and then just divide it by 3. Pretty simple once you get it, and your answer would be 50 sec.
I will assume you mean that the ratio of their corresponding sides is 2 : 5.
the volume of two similar figures is proportional to the cube of their sides
so V1/V2 = 2^3 / 5^3 = 8/125
V1/375 = 8/125
V1 = 24
so time to fill the larger = 375/3 = 125 seconds
time to fill the smaller = 24/3 = 8 seconds
If the two volumes are in the ratio of 2 : 5 then go with the two solutions by Ms. Sue and Shaniqua
(Can you see how important it is to clearly state your problem ?)
To find out how long it will take to fill the smaller prism, we need to determine its volume first.
Given that the ratio of the two similar prisms is 2:5, we can assume that the ratio of their volumes is also 2:5.
So, if the volume of the larger prism is 375 cm³, we can set up the following proportion:
2/5 = x/375
To solve for x, we cross multiply:
2 * 375 = 5 * x
750 = 5x
To isolate x, divide both sides of the equation by 5:
750/5 = x
150 = x
Therefore, the volume of the smaller prism is 150 cm³.
Since sand is being poured into the smaller prism at a rate of 3 cm³ per second, we can divide the volume of the prism by the rate of pouring to find the time it takes to fill it:
150 cm³ / 3 cm³/second = 50 seconds
Hence, it will take 50 seconds to fill the smaller prism.