(a)
To find:the ratio of the surface areas and the ratio of the volumes.
(a)
Answer to Problem 21PPS
The ratio of surface area of prism
Explanation of Solution
Given: Use the two similar prisms at the right.
Calculation:
Consider the height of the rectangular prism
The objective is to find the ratio of the surface areas and the ratio of the volumes of the two figures.
Two solid figures are similar if they have the same shape and their corresponding linear measurements are proportional.
Since both the figures are cylinder and their corresponding linear measurements are proportional, so the cylinders are similar.
The ratio of the length of
The scale factor is
Use the property that if two solids are similar with scale factor of
Thus,
Where
Therefore, the ratio of the surface are is
Now, use the property that if two solids are similar with scale factor of
Thus,
Therefore, the ratio of the volume is
Conclusion:
Therefore, the ratio of surface area of prism
(b)
To find:the surface area of prism
(b)
Answer to Problem 21PPS
The surface area of the rectangular prism
Explanation of Solution
Calculation:
The objective is to find the surface area of the rectangular prism
Put surface of the prism
Therefore, the surface area of the rectangular prism
Conclusion:
Therefore, the surface area of the rectangular prism
(c)
To find:the volume of prism
(c)
Answer to Problem 21PPS
The volume of the rectangular prism
Explanation of Solution
Calculation:
The objective is to find the volume of the rectangular prism
Put volume of the prism
Therefore, the volume of the rectangular prism
Conclusion:
Therefore, the volume of the rectangular prism
Chapter 12 Solutions
Pre-Algebra Student Edition
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