"A block of Granite is in the form of the frustum of a regular square pyramid whose upper and base lower base edges are 3ft and 7ft.., Respectively, if each of the lateral faces is inclined at an angle of 62o 30' to the base , Find the volume of the granite in block"

as seen on the book "Solid Mensuration By Kern And Bland 2nd Edition" #9 page 71

Originally Posted by mventurina1

"A block of Granite is in the form of the frustum of a regular square pyramid whose upper and base lower base edges are 3ft and 7ft.., Respectively, if each of the lateral faces is inclined at an angle of 62o 30' to the base , Find the volume of the granite in block"
as seen on the book "Solid Mensuration By Kern And Bland 2nd Edition" #9 page 71
Hello,

draw a cross-section of the frustrum (see attachment)

With the right triangle(in grey) you'll get: $\displaystyle \frac h2 = \tan(62^\circ30')~\implies~h \approx 3.842'$

Then use the formula to calculate the volume of a frustrum: If $\displaystyle B_l$ denotes the base area and $\displaystyle B_u$ the upper area then the volume is:

$\displaystyle V=\frac h3 \cdot \left(B_l + \sqrt{B_l \cdot B_u}+B_u \right)$

I've got $\displaystyle V \approx 101.173\ cuft$

thank you sir for the accurate answer and for the explanation. !!!

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# A block of granite is in the form of the frustum of a regular square pyramid whose upper and lower base edges are 3 ft. and 7 ft., respectively. If each of the lateral faces is inclined at an angle of 62°30' to the base, find the volume of granite in the

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