6 A can of soup has a 9 cm diameter and is 14 cm high. a What is the radius of the can? b Find the area of a label that wraps around the can. Answer correct to one decimal place. c What is the surface area of the can including the top and bottom of the can? Answer correct to one decimal place.

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a. To find the radius of the can, we can use the formula for the radius of a circle, which is half of the diameter.

Given that the diameter of the can is 9 cm, the radius of the can is half of the diameter, which is $$ \frac{9}{2} = 4.5 $$ cm.

b. To find the area of a label that wraps around the can, we need to find the circumference of the can. The formula for the circumference of a circle is $$ C = 2\pi r $$, where $$ r $$ is the radius of the circle.

Given that the radius of the can is 4.5 cm, the circumference of the can is $$ C = 2\pi 	imes 4.5 $$ cm.

To find the area of the label, we need to multiply the circumference by the height of the can. The formula for the area of a label is $$ A = C 	imes h $$, where $$ h $$ is the height of the can.

Given that the height of the can is 14 cm, the area of the label is $$ A = 2\pi 	imes 4.5 	imes 14 $$ cm$$^2$$.

c. To find the surface area of the can including the top and bottom of the can, we need to find the area of the top and bottom of the can and add it to the area of the label.

The area of the top and bottom of the can is $$ 2 	imes \pi r^2 $$, where $$ r $$ is the radius of the can.

Given that the radius of the can is 4.5 cm, the area of the top and bottom of the can is $$ 2 	imes \pi 	imes 4.5^2 $$ cm$$^2$$.

The total surface area of the can including the top and bottom of the can is the sum of the area of the label and the area of the top and bottom of the can.

Let's calculate the values:
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{9}{2}$$
a. The radius of the can is 4.5 cm.

b. The circumference of the can is $$ C = 2\pi 	imes 4.5 $$ cm.

Let's calculate the circumference:
Calculate the value by following steps:
- step0: Calculate:
  $$2	imes \frac{3141592653589793}{1000000000000000}	imes 4.5$$
- step1: Multiply the terms:
  $$\frac{3141592653589793}{500000000000000}	imes 4.5$$
- step2: Convert the expressions:
  $$\frac{3141592653589793}{500000000000000}	imes \frac{9}{2}$$
- step3: Multiply the fractions:
  $$\frac{3141592653589793	imes 9}{500000000000000	imes 2}$$
- step4: Multiply the terms:
  $$\frac{28274333882308137}{500000000000000	imes 2}$$
- step5: Multiply the terms:
  $$\frac{28274333882308137}{1000000000000000}$$
The circumference of the can is approximately 28.274334 cm.

The area of the label is $$ A = 2\pi 	imes 4.5 	imes 14 $$ cm$$^2$$.

Let's calculate the area of the label:
Calculate the value by following steps:
- step0: Calculate:
  $$2	imes \frac{3141592653589793}{1000000000000000}	imes 4.5	imes 14$$
- step1: Multiply the terms:
  $$\frac{3141592653589793}{500000000000000}	imes 4.5	imes 14$$
- step2: Multiply the terms:
  $$\frac{28274333882308137}{1000000000000000}	imes 14$$
- step3: Reduce the numbers:
  $$\frac{28274333882308137}{500000000000000}	imes 7$$
- step4: Multiply:
  $$\frac{28274333882308137	imes 7}{500000000000000}$$
- step5: Multiply:
  $$\frac{197920337176156959}{500000000000000}$$
The area of the label is approximately 395.840674 cm$$^2$$.

c. The area of the top and bottom of the can is $$ 2 	imes \pi 	imes 4.5^2 $$ cm$$^2$$.

Let's calculate the area of the top and bottom of the can:
Calculate the value by following steps:
- step0: Calculate:
  $$2	imes \frac{3141592653589793}{1000000000000000}	imes 4.5^{2}$$
- step1: Convert the expressions:
  $$2	imes \frac{3141592653589793}{1000000000000000}\left(\frac{9}{2}ight)^{2}$$
- step2: Multiply the terms:
  $$\frac{3141592653589793}{500000000000000}\left(\frac{9}{2}ight)^{2}$$
- step3: Evaluate the power:
  $$\frac{3141592653589793}{500000000000000}	imes \frac{9^{2}}{2^{2}}$$
- step4: Multiply the fractions:
  $$\frac{3141592653589793	imes 9^{2}}{500000000000000	imes 2^{2}}$$
- step5: Multiply:
  $$\frac{254469004940773233}{2000000000000000}$$
The area of the top and bottom of the can is approximately 127.234502 cm$$^2$$.

The total surface area of the can including the top and bottom of the can is the sum of the area of the label and the area of the top and bottom of the can.

Let's calculate the total surface area:
Calculate the value by following steps:
- step0: Calculate:
  $$395.840674+127.234502$$
- step1: Add the numbers:
  $$523.075176$$
The total surface area of the can including the top and bottom of the can is approximately 523.075176 cm$$^2$$.
a. The radius of the can is 4.5 cm. b. The area of the label is approximately 395.8 cm². c. The surface area of the can, including the top and bottom, is approximately 523.1 cm².

6 A can of soup has a 9 cm diameter and is 14 cm high. a What is the radius of the can? b Find the area of a label that wraps around the can. Answer correct to one decimal place. c What is the surface area of the can including the top and bottom of the can? Answer correct to one decimal place.

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