Question

Solid mensuration question. Medal will be awarded promise :) i need help .....

A plane is passed through a regular hexagonal pyramid whose base edge measures 8 inches. If the section formed, 6 inches from the base, is parallel to the base and has an area of 18.5 square inches. Find the volume and the lateral area of the pyramid .?

Answer 1

hi @OtherWorldly can you help me ? :)

Answer 2

Srry I don't know @jake4272 @ganeshie8 @welshfella

Answer 3

the area of a regular hexagon = (3 sqrt3)a^2 / 2 where a is the side length
the volume of this regular pyramid = (1/3)* area of base * height
so for this pyramid its (1/3) (3 sqrt3 / 2) *8^2 * h = 32 sqrt3 h sq ins.

Answer 4

32 sqrt3 is the h ?

Answer 5

No h is the height of the pyramid 32 sqrt3 h its its volume ( in cubic inches)

Answer 6

I'm struggling with this one.....

Answer 7

yeah :( i really struggling to this question ,

Answer 8

what i thought to do is to use the fact that ratio of the volumes = ratios of the cubes of their heights but that will give a complicated equation...

Answer 9

the section will create a small pyramid with volume (1/3) * 18.5 * (h - 6) = 6.167h - 37 cu ins

giving 6(1.167h - 37 )/ 32 sqrt3h = (h - 6)^3 / h^3 and solve for h

Answer 10

the first pyramid , can i solve the volume ,height , slant height with the base edge 8 ,?

Answer 11

we dont know the height of first one if we find that we have solved the whole problem

Answer 12

we could solve that equation with a graphical calculator or a math tool like mathematica.
But i have a feeling there is an easier way to do this.

Answer 13

hmm ? can i use the frustum ?

Answer 14

not sure

suppose we take a vertical slice through the middle of the pyramid and use similar triangles