a In similar solids, corresponding linear measures have equal ratios. The common ratios are called the scale factor.
B
b Begin by finding the height of the larger can. Then, use the formula of the volume of a cylinder.
A
a 10:13
B
b ≈ 419.6 cm^3
Practice makes perfect
a We have two cylindrical cans of tuna. The small can has a radius of 4 centimeter and a height of 3.8 centimeters. The larger can has a radius of 5.2 centimeters, and we will let h be its height.
We will find the scale factor of the cylinders. In similar solids, the corresponding linear measures have equal ratios. These common ratios are called the scale factor. In this case, the ratio of the radii will give us the scale factor.
Scale Factor
4/5.2=10/13 ⇔ 10:13
The scale factor of the cylinders is 10:13.
The height of the larger can is 4.94 centimeters. From here we can find its volume using the formula of the volume of a cylinder.
V= π r^2 h
Let's substitute r=5.2 and h=4.94 into the formula and simplify it.
