A sheet ABCD of dimensions 10 ft x 3 ft is shown in Figure A-6.1. A box is made by removing two squares of e dimensions AEFG and DHIJ and two rectangles of equal dimensions BKLM and CNOP respectively.
Answers
Answer:
Step-by-step explhttps://media.cheggcdn.com/study/71e/71e051d7-61d3-4367-9558-91c4cb93f46f/imageanation:
Given : A sheet ABCD of dimensions 10 ft x 3 ft is shown in Figure A-6.1. A box is made by removing two squares of e dimensions AEFG and DHIJ and two rectangles of equal dimensions BKLM and CNOP respectively.
To Find : Volume of the box
How many soap bars of volume 5-x can be fitted.
Solution:
Dimension = 10 * 3
Square cut = x by x
Dimensions = (10 - 2x )/ 2 = 5 - x ( length base and top
3 - 2x ( width )
x height
Volume = (5 - x)(3 - 2x) x
= (15 +2x² - 13x)x
= 2x³ - 13x² + 15x
Volume of the box is 2x³ - 13x² + 15x
x = 0.5
=>
Volume of the box = (5 - x)(3 - 2x) x
= ( 4.5) ( 2) (0.5)
= 4.5 cubic feet
Bar soap of 5 -x hence can be fitted max = (5 - x)(3 - 2x) x / ( 5 - x)
= (3 - 2x) x
= 2x(1.5 - x)
Hence correct options are :
Volume of the box is 2x³ - 13x² + 15x
At most 2x(1.5 - x) soap bars can be fitted
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