Scale Factor, Area and Volume

A cone has a surface area 360π $$in^2$$ and a volume of 800π $$in^3$$ . The cone is dilated and the surface area of the dilated cone is 2,250π $$in^2$$ . What is the dilated cone's volume in cubic inches?

A government agency is redesigning a satellite, or an object that goes in orbit around Earth. The surface of the satellite is covered with solar panels that supply the satellite with energy. The interior of the satellite is filled with scientific instruments. In the current design, the satellite has a surface area of 5.4 square feet and a volume of 1.2 cubic feet.

If the agency wants to increase the surface area to 48.6 square feet so the satellite can generate more energy, by what scale factor do they need to dilate the satellite? _

(a)  

A food company is designing boxes for several products. Each box is a rectangular prism. The company makes a single serving cereal box that contains 1.2 ounces of cereal. They plan to make an extra large box for school cafeterias. The extra large box will be a dilation of the single serving box using a scale factor of 4. How many ounces of cereal will the extra large box contain in ounces of cereal?

A food company is designing boxes for several products. Each box is a rectangular prism. The company also wants to offer a family size box of cereal. The family size box will be a dilation of the single serving 1.2-ounce box. It must contain 18.75 ounces of cereal. What scale factor does the company need to use for the family size box?

When multiplying a length by a scale factor, does the scale factor change? ​ (a)   When adjusting the surface area of a solid, the scale factor must be ​ (b)   . When adjusting the volume of a solid, the scale factor must be​ (c)