Question

1-A right cylinder has radius 9 cm and height 12 cm. If the radius and height are tripled, what happens to the surface area?

The surface area is multiplied by 6.
The surface area is multiplied by 9.
The surface area is multiplied by 1/3.
The surface area is tripled.

2-A right rectangular prism has length 4 cm, width 2 cm, and height 7 cm. If the length, width, and height are halved, what happens to the surface area?

The surface area is multiplied by 4.
The surface area is multiplied by 1/2.
The surface area is multiplied by 1/4.
The surface area is doubled.

Answer 1

(1) As we know that the surface area of the cylinder is given by the formula

surface Area=
`2\pi rh+2 \pi r^2`

If the radius and height are tripled, then we get

surface Area=
`2\pi *3r*3h+3*2 \pi (3r)^2`

surface are =
`9*2\pi rh+9*2 \pi (r)^2=9(2\pi rh+2 \pi (r)^2)`

The surface area is multiplied by 9.

(2) As we know that the surface area of the rectangular prism is given by

Surface area=
`2(wl+hl+hw)\\`

Now if the length, width, and height are halved, we get the surface area as

surface area=
`2((1)/(4)wl+(1)/(4)hl+(1)/(4)hw) =2*(1)/(4)(wl+hl+hw)\\`

surface area=
`(1)/(2)(wl+hl+hw)\\`

The surface area is multiplied by 1/2.