Describe how the change affects the surface area and volume of the solid.

Question

Describe how the change affects the surface area and volume of the solid.

31.Tripling the radius and height of a cylinder

32.Dividing all the dimensions of a prism by 4.

33. Multiplying all the dimensions of a pyramid by a scale factor of 5.

34.Multiplying all the dimensions of a cone by ½.

36.A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all changed to half of their original size, what will be the new volume of the rectangular solid?

37.If the surface area of a cube is increased by a factor of 49, what is the change in the length of the sides of the cube?

Answer 1

The ratio of area of similar figures is as the ratio of the square of the scale factor.

The ratio of the volumes of similar figures is as the ration of the cube of the scale factor.

Answer 2

31.Tripling the radius and height of a cylinder

scale factor is 3, so SA increases by factor of 9 and volume increases by scale factor of 27

32.Dividing all the dimensions of a prism by 4.

scale factor is 1/4, so SA decreases by factor of 1/16 and volume decreases by scale factor of 1/64

33. Multiplying all the dimensions of a pyramid by a scale factor of 5.

scale factor is 5, so SA increases by factor of 25 and volume increases by factor of 125

34.Multiplying all the dimensions of a cone by ½.

scale factor is 1/2, so SA is multiplied by 1/4 and volume is multiplied by 1/8

36.A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all changed to half of their original size, what will be the new volume of the rectangular solid?

if l, w and h all 1/2, then volume will be 1/8 or 3 cu dec

37.If the surface area of a cube is increased by a factor of 49, what is the change in the length of the sides of the cube?

since surface area is square of scale factor then length will have a scale factor of 7