The plaster cast

The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area.

Correct answer:

V =  29.4628 m3
S =  68.3013 m2

Step-by-step explanation:

a=5 m S1=a2=52=25 m2  a2 = (a/2)2+h12  h1=a2(a/2)2=52(5/2)24.3301 m  h12 = h22 + (a/2)2  h2=h12(a/2)2=4.33012(5/2)23.5355 m  V=31 S1 h2=31 25 3.5355=29.4628 m3
S2=21 a h1=21 5 4.330110.8253 m2  S=4 S2+S1=4 10.8253+25=68.3013 m2

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
See also our right triangle calculator.
Calculation of an equilateral triangle.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: