A roll of paper towels has a radius of 12 cm and a height of 18 cm. the cardboard tube in the centre has a radius of 5cm.
Find the volume of the paper towels
So would I do 18-12?
why ever would you subtract radius from height?
The volume of towels is the volume of the whole package, minus the volume of the inner cylinder. Recall that the volume of a cylinder is v = πr^2 h. So, the volume of the towels is
π*12^2*18 - π*5^2*18 = 2142π cm^3
No, to find the volume of the paper towels, you would need to calculate the volume of the entire roll, including the inner cardboard tube.
To do this, you can treat the roll as a cylinder with two different radii - one for the outer edge of the roll and one for the inner edge (cardboard tube).
First, let's find the volume of the paper towels without the cardboard tube. The formula for the volume of a cylinder is:
Volume = π * r^2 * h
where r is the radius and h is the height.
For the paper towels, the radius (r) is 12 cm and the height (h) is 18 cm. Plugging these values into the formula, we have:
Volume of paper towels = π * (12 cm)^2 * 18 cm
Next, let's find the volume of the cardboard tube. Again, we will use the same formula for the volume of a cylinder but with the radius of the cardboard tube (5 cm) and the height of the roll (18 cm):
Volume of cardboard tube = π * (5 cm)^2 * 18 cm
Finally, to find the total volume of the paper towels, we need to add the volume of the paper towels and the volume of the cardboard tube together:
Total volume of paper towels = Volume of paper towels + Volume of cardboard tube
I hope this explanation helps!