Middle School

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1. April has two cone-shaped containers. The first container has a diameter of 6 inches and a height of 4 inches. The second container has a radius of 4 inches and a height of 3 inches. Which statement is true about the containers?

A. The first container will hold about 100 cubic inches more than the second container.
B. The second container will hold about 13 cubic inches more than the first container.
C. The first container will hold about twice as much as the second container.
D. Both containers will hold the same amount.

2. A cake decorator rolls a piece of stiff paper to form a cone. She cuts off the tip of the cone and uses it as a funnel to pour decorator sprinkles into small containers. The cone has a radius of 6 cm and a height of 18 cm. What is the volume of the cone before the end is cut off?

Answer :

The second container will hold about 13 cubic inches more than the first container.(Option B)

To compare the volumes of the two cone-shaped containers, we can use the formula for the volume of a cone:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

For the first container:

- Diameter = 6 in. (so, radius [tex]\( r_1 = \frac{6}{2} = 3 \)[/tex] in.)

- Height = 4 in.

[tex]\[ V_1 = \frac{1}{3} \pi (3)^2 \times 4 = \frac{1}{3} \pi \times 9 \times 4 = 12 \pi \][/tex]

For the second container:

- Radius = 4 in.

- Height = 3 in.

[tex]\[ V_2 = \frac{1}{3} \pi (4)^2 \times 3 = \frac{1}{3} \pi \times 16 \times 3 = 16 \pi \][/tex]

Now, let's compare the volumes:

[tex]\[ V_1 = 12 \pi \][/tex]

[tex]\[ V_2 = 16 \pi \][/tex]

Since [tex]\( \pi \)[/tex] is the same in both volumes, we can compare them directly:

[tex]\[ V_2 - V_1 = 16 \pi - 12 \pi = 4 \pi \][/tex]

Now, let's calculate the numerical value of [tex]\( 4 \pi \)[/tex]: [tex]\[ 4 \pi \approx 12.5664 \][/tex]

So, the second container will hold about 12.5664 cubic inches more than the first container.

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Rewritten by : Barada

Answer:

I would say for 1. would be A

And i think... that 2. is 3 i'm not sure that's all i really know

Step-by-step explanation: