Question

100 POINTS!!!!!

Answer 1

Answer:

a. Ratio of their circumference = 2:3

b. The ratio of their surface areas = 2:3

c. The ratio of their volume = 4:9

Step-by-step explanation:

Let the cylinders be labelled as A and B respectively.

Diameter of cylinder A = 6 in,

its radius = $\frac{diameter}{2}$

                = $\frac{6}{2}$ = 3 in

Diameter of cylinder B = 9 in,

its radius = $\frac{diameter}{2}$

               = $\frac{9}{2}$  = 4.5 in

Thus,

a. circumference of a circle = 2$\pi$r

Circumference of cylinder A = 2$\pi$r

                                               = 2 x $\pi$ x 3

                                            = 6$\pi$ in

Circumference of cylinder B = 2$\pi$r

                                              = 2 x $\pi$ x 4.5

                                              = 9$\pi$

Ratio of their circumference = $\frac{circumference of cylinder A}{circumference of cylinder B}$

                                               = $\frac{6\pi }{9\pi }$

                                               = 2:3

b. The surface area of a cylinder = 2$\pi$rh

the surface area of cylinder A = 2$\pi$rh

                                                  = 6$\pi$h

the surface area of cylinder B = 2$\pi$rh

                                                = 9$\pi$h

The ratio of their surface areas = $\frac{surface area of cylinder A}{surface area of cylinder B}$

                                                 = $\frac{6\pi h}{9\pi h}$

                                                 = 2:3

c. Volume of a cylinder = $\pi$$r^{2}$h

volume of cylinder A = $\pi$$r^{2}$h

                                = $\pi$ x $3^{2}$ x h

                                = 9$\pi$h

volume of cylinder b = $\pi$$r^{2}$h

                                    = $\pi$ x $4.5^{2}$ x h

                                    = 20.25$\pi$h

The ratio of their volume = $\frac{volume of cylinder A}{volume of cylinder B}$

                                         = $\frac{9\pi h}{20.25\pi h}$

                                         = 4:9