(A) Find the volume V of the described solid S. A pyraid with height h and base

Question

(A) Find the volume V of the described solid S.

A pyraid with height h and base an equilateral triangle with side a (a tetrahedron).

(B) Find the volume V of the described solid S.

The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base are squares.

(C) Find the volume V of the described solid S.

The base of S is the region enclosed by the parabola y = 4 - 2x^2 and the x-axis. Cross sections perpendicular to the y-axis are squares.

Please answer with work shown.

Explanation / Answer

a) volume = 1/3 base area x height = root(3) / 4 a^2 h

b) volume = base area x heigth = 16pi r^2 x 4r = 64pir^3

c) for this question u need to do integration : integral ( 4 x^2)(4x^2)dx = 16/5x^5 put x = root(2);

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