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

Explanation:

Step1: Calculate ratio for given cylinder

For the cylinder with radius $r = 2.8$ inches and height $h=2.4$ inches, the ratio of radius to height is $\frac{r}{h}=\frac{2.8}{2.4}=\frac{7}{6}$.

Step2: Calculate ratios for each option

• Option 1: For radius $r_1 = 1.8$ inches and height $h_1 = 1.4$ inches, $\frac{r_1}{h_1}=\frac{1.8}{1.4}=\frac{9}{7}$.
• Option 2: For radius $r_2 = 1.4$ inches and height $h_2 = 1.2$ inches, $\frac{r_2}{h_2}=\frac{1.4}{1.2}=\frac{7}{6}$.
• Option 3: For radius $r_3 = 5.6$ inches and height $h_3 = 4.2$ inches, $\frac{r_3}{h_3}=\frac{5.6}{4.2}=\frac{4}{3}$.
• Option 4: No height is given for the last - option, so we can't calculate its ratio.

Answer:

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