A right pyramid has a square base with side of base 4 cm and the height of prism is 9 am. The pyramid is cut in three parts of equal heights by two planes parallel to its base. What is the ratio of the volume of the top, middle and the bottom part respectively?
Answers
Answer:
The required ratio is 1 : 7 : 19.
Step-by-step-explanation:
Given,
Pyramid has a square base of side 4 cm.
Height of the prism is 9 cm.
= > Slant height of the pyramid^2 = ( 9 cm )^2 + ( 4 / 2 cm )^2
= > Slant height of the pyramid^2 = 81 cm^2 + 4 cm^2
= > Slant height of the pyramid^2 = 85 cm^2
When pyramid is cut in three parts of equal height, height of each part becomes ( 9 / 3 ) cm i.e. 3 cm.Also, length of slope of each part becomes √85 / 3 cm i.e. √( 85 / 9 ) cm.
Thus,
= > Half of length of base of 1st part i.e. pyramid of height 3 cm = √[ √{ 85 / 9 } cm )^2 - ( 3 cm )^2 }
= > Length of base of 1st part = 2 x √{ 85 / 9 cm^2 - 9 cm^2 }
= > Length of base of 1st part = 2 x √{ ( 85 - 81 ) / 9 }
= > Length of base of 1st part = 2 x √{ 4 / 9 }
= > Length of base of 1st part = 2 x 2 / 3
Slant height of pyramid is √85. So, slant height of pyramid in 1st part is 2 / 3 of √85 that is √( 340 / 9 ).
So, length of base of 2nd pyramid of height 6 cm is 2 x 4 / 3 cm.
Thus,
= > Required ratio
= > 1 / 3 x ( length x breadth x height ) of 1st part : 1 / 3 x ( length x breadth x height ) of 2nd part : 1 / 3 x ( length x breadth x height ) of 3rd part
= > ( length x breadth x height ) of 1st part : { ( length x breadth x height ) of 2nd and 1st part - ( length x height x breadth ) of 1st part } : { ( length x breadth x height ) of 3rd part, 2nd part and 1st part ) - ( length x height x breadth ) of 2nd and 1st part }
= > { ( 2 x 2 / 3 ) x ( 2 x 2 / 3 ) x 3 } : [ ( 2 x 4 / 3 x 2 x 4 / 3 x 6 ) - ( 2 x 2 / 3 x 2 x 2 / 3 x 3 ) ] : [ 4 x 4 x 9 - ( 2 x 4 / 3 x 2 x 4 / 3 x 6 ) ]
= > 16 / 3 : ( 128 / 3 - 16 / 3 ) : ( 144 - 128 / 3 )
= > 64 : 112 : 304
= > 1 : 7 : 19
Hence the required ratio is 1 : 7 : 19.
Answer:
cost of 4 pens 6 notebooks and 9 files is 305 rupees, the cost of 3 pens 4 notebooks and two files is 145 rupees find the cost of 5 pens 8 notebooks and 16 files
Step-by-step explanation:
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