(a)
To find: The surface area and the volume of the prism.
(a)
Answer to Problem 31PPS
The surface area of the prism is
Explanation of Solution
The surface area of the prism is calculated as,
The volume of the prism is calculated as,
Therefore, the surface area of the prism is
(b)
To find: The surface area and the volume of the prism for dilation of scale factor of
(b)
Answer to Problem 31PPS
The surface area of the prism after dilation is
Explanation of Solution
The new dimension after dilation is,
The surface area of the prism is calculated as,
The volume of the prism is calculated as,
Therefore, the surface area of the prism after dilation is
(c)
To find: The surface area and the volume of the prism for dilation of scale factor of
(c)
Answer to Problem 31PPS
The surface area of the prism after dilation is
Explanation of Solution
The new dimension after dilation is,
The surface area of the prism is calculated as,
The volume of the prism is calculated as,
Therefore, the surface area of the prism after dilation is
(d)
To find: The number of times the surface area and volume of the image is after each dilation.
(d)
Answer to Problem 31PPS
The number of times the surface area and volume of the image is after each dilation is mentioned below.
Explanation of Solution
For scale factor 2.
For scale factor
For scale factor 2.
For scale factor
(e)
To make: The conjecture on surface area and volume of prism due to dilation.
(e)
Answer to Problem 31PPS
The conjecture is stated below.
Explanation of Solution
From the obtained result.
Surface area will have effect by
Volume will have effect by
Chapter 9 Solutions
Geometry, Student Edition
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