Two similar cylindrical cans have heights 2m and 3m respectively. If the smaller one holds 800g of sugar, how many kilogram of sugar will the bigger one hold?
We know that the two cans are similar, which means they have the same shape but different sizes. The volume of a cylinder is given by the formula V=πr^2h, where r is the radius and h is the height.
Let's assume that the radius of the smaller can is r1 and the radius of the bigger can is r2. We need to find the value of r2 so that we can use the formula to calculate the volume of the bigger can.
We can use the fact that the two cans are similar to set up a proportion:
r1 / r2 = 2 / 3
Cross-multiplying this proportion, we get:
3r1 = 2r2
Solving for r2, we get:
r2 = (3/2) r1
Now we can use the formula to calculate the volume of the smaller can:
V1 = πr1^2h1 = π( r1^2)(2) = 4πr1^2
And we know that this can holds 800g of sugar. Let's convert this to kilograms:
800g = 0.8kg
So the density of sugar is:
ρ = m/V = 0.8kg / (4πr1^2) = 0.2 / π r1^2
Now we can use this density to calculate the mass of sugar that the bigger can can hold. The volume of the bigger can is:
V2 = πr2^2h2 = π((3/2)r1)^2(3) = 13.5πr1^2
The mass of sugar that this can can hold is:
m = ρV2 = 0.2 / π r1^2 * 13.5πr1^2 = 2.7kg
Therefore, the bigger can can hold 2.7kg of sugar.