When two solids are similar, the ratio of their surface areas is equal to the ratio of their corresponding linear measures squared, and the ratio of their volumes is equal to the ratio of their corresponding linear measures cubed.
We will use the knowledge that these prisms are similar to find the suface area and volume of the bigger solid. We will do these things one at a time.
Surface Area
When two solids are similar, the ratio of their surface areas is equal to the ratio of their corresponding linear measures squared.
Surface area of the smaller solid/Surface area of the bigger solid
=
(Height of the smaller solid/Height of the bigger solid)^2
We know that the height and the surface area of the smaller solid are 2 yards and 13 square yards, respectively. We also know that the height of the bigger solid is 4 yards. If we let S be the surface area of the bigger solid, we can substitute these values into this equation and solve for S.
Surface area of the smaller solid/Surface area of the bigger solid=(Height of the smaller solid/Height of the bigger solid)^2
The surface area of the bigger rectangular prism is 52 square yards.
Volume
When two solids are similar, the ratio of their volumes is equal to the ratio of their corresponding linear measures cubed.
Volume of the smaller solid/Volume of the bigger solid
=
(Height of the smaller solid/Height of the bigger solid)^3
We know that the height and the volume of the smaller solid are 2 yards and 3 cubic yards, respectively. We also know that the height of the bigger solid is 4 yards. If we let V be the volume of the bigger solid, we can substitute these values in this equation and solve for V.
Volume of the smaller solid/Volume of the bigger solid=(Height of the smaller solid/Height of the bigger solid)^3
