Question

a cylinder has a radius of 2.8 inches and a height of 2.4 inches. which cylinder is similar?

Explanation:

Step1: Find the ratio of radius to height of the given cylinder

The given cylinder has radius $r = 2.8$ inches and height $h=2.4$ inches. The ratio $\frac{r}{h}=\frac{2.8}{2.4}=\frac{7}{6}$.

Step2: Check the ratio for each option

Option 1:

Radius $r_1 = 1.8$ inches and height $h_1=1.4$ inches. The ratio $\frac{r_1}{h_1}=\frac{1.8}{1.4}=\frac{9}{7}
eq\frac{7}{6}$.

Option 2:

Radius $r_2 = 1.4$ inches and height $h_2 = 1.2$ inches. The ratio $\frac{r_2}{h_2}=\frac{1.4}{1.2}=\frac{7}{6}$.

Option 3:

Radius $r_3 = 5.6$ inches and height $h_3=4.2$ inches. The ratio $\frac{r_3}{h_3}=\frac{5.6}{4.2}=\frac{4}{3}
eq\frac{7}{6}$.

Option 4:

Radius $r_4 = 2.4$ inches and height $h_4 = 2.8$ inches. The ratio $\frac{r_4}{h_4}=\frac{2.4}{2.8}=\frac{6}{7}
eq\frac{7}{6}$.

Answer:

The cylinder with a radius of 1.4 inches and a height of 1.2 inches is similar.