Answer :
Answer:
[tex]365.61cm^3[/tex]
Step-by-step explanation:
Start by finding the volume of the cylinder can using the volume formula for a cylinder: [tex]V=\pi r^2h[/tex].
Recalling that diameter is twice the radius, the radius is 7/2 or 3.5.
Plugging in the given values, the volume is,
[tex]V=\pi (3.5)^2(10)=384.85[/tex]
This isn't the final answer, remember that 5% of that volume is filled with air, so 5% of the solved volume must be removed to get the correct answer!
V = 384.85 - (0.05)384.85 = 365.61
Another way to solve this is to multiply the solved volume by 95% or 0.95 since that's how much room for soup remains after 5% of it being filled with air.
The volume of soup inside the can is 365.8 cubic centimeters, after accounting for 5% of the space taken up by air.
To find the volume of soup inside a can with a diameter of 7 cm and a height of 10 cm, where 5% of the space is taken up by air, we first calculate the volume of the entire can using the formula for the volume of a cylinder: V =
πr²h. The radius (r) is half of the diameter, so r = 7 cm / 2 = 3.5 cm. The height (h) is given as 10 cm.
Now we calculate the total volume: V = π × (3.5 cm)² × 10 cm = 385.0 cm³. Since 5% of this volume is air, we need to determine the volume of soup, which is 95% of the total volume. We calculate this as 0.95 × 385.0 cm³ = 365.75 cm³ of soup.
To provide the answer to the nearest tenth, we round off 365.75 to 365.8 cm³.
