Number of ounces left is 1120
Step-by-step explanation:
- Step 1: Find number of ounces left after each day.
Given total soup prepared each day = 15 gallons
Amount served each day = 1/4 of 15 = 15/4 gallons
Amount left after each day = 15 - 15/4 = 60 - 15/4 = 35/4 gallons
- Step 2: Convert gallons into ounces. 1 gallon = 128 ounces
35/4 gallons = 35/4 × 128 = 1120 ounces
Given:
Surface area = 4,362 yards
Length = 36 yard
Width = 21 yard
Height = c
To find:
Volume of the rectangular prism.
Solution:
Surface area formula:
![SA = 2(lw+wh+lh)](https://tex.z-dn.net/?f=SA%20%3D%202%28lw%2Bwh%2Blh%29)
Substitute the given values.
![4362 = 2(36\times21 +21 \times c+36 \times c)](https://tex.z-dn.net/?f=4362%20%3D%202%2836%5Ctimes21%20%2B21%20%5Ctimes%20c%2B36%20%5Ctimes%20c%29)
![4362 = 2(756+21 c+36 c)](https://tex.z-dn.net/?f=4362%20%3D%202%28756%2B21%20%20c%2B36%20c%29)
![4362 = 2(756+57c)](https://tex.z-dn.net/?f=4362%20%3D%202%28756%2B57c%29)
![4362 = 1512+114c](https://tex.z-dn.net/?f=4362%20%3D%201512%2B114c)
Subtract 1512 from both sides.
![4362- 1512 = 1512+114c - 1512](https://tex.z-dn.net/?f=4362-%201512%20%3D%201512%2B114c%20-%201512)
![2850=114c](https://tex.z-dn.net/?f=2850%3D114c)
Divide by 114 on both sides, we get
25 = c
Height = 25
Volume = length × breadth × height
= 36 × 21 × 25
= 18900
Volume of rectangular prism is 18900 cubic yards.
Answer: The surface area is reduced by a factor of 16/25
Step-by-step explanation: The area is the square measurements. So squaring the factor of the linear measurement change is the quick way is to determine the factor for the area.
The longer way-- if you had to prove your conclusion:
Compute the area of each side, add all the five sides of the prisms and find the ratio.
The area of the large prism is 500 square units.
The area of the smaller prism is 320 square units
320/500 = 32/50, reduce again 16/25