Video Transcript
Suppose the large container is to be filled with rice using the small container. How many times would the small container need to be filled to completely fill the
large container? Give your solution to one decimal place.
In this question, both the small and large containers are cylinders. And we recall that the volume of a cylinder, 𝑉, can be calculated using the formula
𝑉 is equal to 𝜋𝑟 squared ℎ, where 𝑟 is the radius and ℎ is the height of the
cylinder.
In this question, we need to calculate how many times the small container needs to be
filled to completely fill the large container. We will begin by calculating the volume of the small cylinder. Since the diameter of the small container is 10.9 centimeters, then its radius is
half of this. This is equal to 5.45 centimeters.
The small container has a height of 12 centimeters. Therefore, its volume is equal to 𝜋 multiplied by 5.45 squared multiplied by 12. This is equal to 356.43𝜋 cubic centimeters. We will now repeat this process for the large container. The large container has a radius of 9.95 centimeters. Its height is the same as the small container, that is, 12 centimeters. Therefore, its volume is equal to 𝜋 multiplied by 9.95 squared multiplied by 12,
which equals 1188.03𝜋 cubic centimeters.
We now have the volume of both containers. Every time we transfer rice from the small container to the large one, we add
356.43𝜋 cubic centimeters. We need to calculate how many times we need to do this to completely fill the large
one. This can be done by finding the quotient of the two values. We need to divide the volume of the large container by the volume of the small
container. We have 1188.03𝜋 divided by 356.43𝜋. We begin by canceling the shared factor of 𝜋 from the numerator and denominator. Dividing 1188.03 by 356.43 gives us 3.3331 and so on.
We are asked to round our answer to one decimal place. We can therefore conclude that the small container needs to be filled 3.3 times in
order to completely fill the large container with rice.
