[Solid Mensuration] please help meeee!! :)

(Rofl) Please help me on how to solve diz XD

"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 62^{o} 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

Thanks in advance !!(Hi)

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Re: [SolidMensuration] please help meeee!! :)

Quote:

Originally Posted by

**mventurina1** (Rofl) Please help me on how to solve diz XD

"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 62^{o} 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

Thanks in advance !!(Hi)

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 $\displaystyle V \approx 101.173\ cuft$

Re: [Solid Mensuration] please help meeee!! :)

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