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Question Video: Cylinders in a Real-World Context Mathematics • 8th Grade

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.

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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 πœ‹π‘Ÿ squared β„Ž, where π‘Ÿ is the radius and β„Ž 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œ‹ multiplied by 5.45 squared multiplied by 12. This is equal to 356.43πœ‹ 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œ‹ multiplied by 9.95 squared multiplied by 12, which equals 1188.03πœ‹ 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œ‹ 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œ‹ divided by 356.43πœ‹. We begin by canceling the shared factor of πœ‹ 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.

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