Question

a cylindrical piece of cheese is cut in half vertically. the piece of cheese has a diameter of 5 inches and a height of 3 inches. find the perimeter of the cross - section formed by the cut. type only the number answer, dont worry about the units.
a) 13
b) 16
c) 15
d) 7.5
the diagram shows a block of processed cheddar cheese that has a mass of 542 grams. find the density of processed cheddar cheese to the nearest hundredth of a gram per cubic centimeter. just type the number answer and dont worry about typing the units.
b) 5.50
d) 8.10
6.78
7.25

Explanation:

Step1: Analyze cross - section of cylinder

When a cylinder is cut vertically, the cross - section is a rectangle. The length of the rectangle is the height of the cylinder and the width is the diameter of the cylinder.

Step2: Identify dimensions

The diameter of the cylinder (width of rectangle) $d = 5$ inches and the height of the cylinder (length of rectangle) $h=3$ inches.

Step3: Calculate perimeter of rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$. Here, $l = 3$ inches and $w = 5$ inches. So $P=2(3 + 5)=16$ inches.

for density problem:

Step1: Calculate volume of rectangular - prism cheese

The volume formula for a rectangular prism is $V=l\times w\times h$. Given $l = 8$ cm, $w = 2$ cm and $h = 5$ cm. So $V=8\times2\times5=80$ $cm^{3}$.

Step2: Calculate density

The density formula is $
ho=\frac{m}{V}$, where $m = 542$ grams and $V = 80$ $cm^{3}$. So $
ho=\frac{542}{80}=6.775\approx6.78$ $g/cm^{3}$.

Answer:

b) 16