SOLUTION: A concrete gate post comprises a right rectangular prism .length of sides of a rectangular prism (having a square base and a pyramid on top) is 30cm and the height of the rectangul

Algebra ->  Volume -> SOLUTION: A concrete gate post comprises a right rectangular prism .length of sides of a rectangular prism (having a square base and a pyramid on top) is 30cm and the height of the rectangul      Log On


   

Question 1098602: A concrete gate post comprises a right rectangular prism .length of sides of a rectangular prism (having a square base and a pyramid on top) is 30cm and the height of the rectangular section is 150cm. perpendicular height of the pyramid section is 8cm. What is the volume of concrete required to make ONE post?
Surface area of the pyramid section of the post?
If the length of sides of base is halved, how many posts,having the same design can be made with the same volume of concrete as the original post
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of pyramid = 1/3 *s^2*h
V= 1/3 *30^2*8= 2400 cm^3
Volume of cylindrical portion l*b*h
V= 30*30*150= 135000 cm^3
TOTAL volume =137400 cm^3
Surface area of the pyramid section of the post=4 pi r l
4*area of one triangle
4*1/2 *30*17=1020 cm^2
The base is reduced by 1/2 - prism
If the edges are halved they will become 15 cm each. Volume now will be (15*15*150
=33750 cm^3
pyramid volume
1/3*15*15*8=600 cm^3
prism volume = 15*15*150=34350 cm^3
Number of posts =137400/34350 =4 posts from the same volume of concrete