Question

you are pouring juice into a cylindrical cup with a 2 inch radius and height of 8 inches. if you want to fill it exactly half full, how many cubic inches of juice should you pour in?
100.8 cubic inches
16 cubic inches
25.13 cubic inches
50.3 cubic inches

Explanation:

Step1: Calculate the volume of the full - cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(r = 2\) inches and \(h=8\) inches.

$$V=\pi\times(2)^{2}\times8=\pi\times4\times8 = 32\pi$$

Step2: Calculate the volume of the half - filled cylinder

Since we want half of the volume, \(V_{half}=\frac{1}{2}\times V\). Substitute \(V = 32\pi\) into the formula.

$$V_{half}=\frac{1}{2}\times32\pi=16\pi$$

Take \(\pi\approx3.14\), then \(V_{half}=16\times3.14 = 50.24\approx50.3\)

Answer:

50.3 cubic inches