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A can of soup has a diameter of 7 cm and a height of 11 cm. Assuming that the can is full, what is the volume of soup contained in the can? Use 3.14 for π and round your answer to the nearest cubic centimeter.A.423 cm3B.1692 cm3C.242 cm3D.135 cm3

Question

A can of soup has a diameter of 7 cm and a height of 11 cm. Assuming that the can is full, what is the volume of soup contained in the can? Use 3.14 for π and round your answer to the nearest cubic centimeter.A.423 cm3B.1692 cm3C.242 cm3D.135 cm3

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Solution

To find the volume of the can of soup, we need to use the formula for the volume of a cylinder, which is:

V=πr2h V = \pi r^2 h

where:

  • V V is the volume,
  • π \pi (pi) is approximately 3.14,
  • r r is the radius of the base of the cylinder,
  • h h is the height of the cylinder.

Given:

  • The diameter of the can is 7 cm, so the radius r r is half of the diameter: r=72=3.5 cm r = \frac{7}{2} = 3.5 \text{ cm}
  • The height h h of the can is 11 cm.

Now, plug these values into the formula:

V=3.14×(3.5)2×11 V = 3.14 \times (3.5)^2 \times 11

First, calculate (3.5)2 (3.5)^2 :

(3.5)2=3.5×3.5=12.25 (3.5)^2 = 3.5 \times 3.5 = 12.25

Next, multiply this result by 3.14:

3.14×12.25=38.465 3.14 \times 12.25 = 38.465

Finally, multiply by the height (11 cm):

38.465×11=423.115 38.465 \times 11 = 423.115

Rounding to the nearest cubic centimeter:

423.115423 423.115 \approx 423

So, the volume of the soup contained in the can is approximately 423 cubic centimeters.

The correct answer is: A. 423 cm³

This problem has been solved

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