Question

Find the volume V of the described solid S. A frustum of a pyramid with square base of side b, square top of side a, and height h a b V = What happens if a = b? (Enter your answer in terms of b and h.) We get a ---Select-- with volume V = What happens if a = 0? (Enter your answer in terms of b and h.) We get a ---Select--- with volume V =

Please provide clear explanation as I need to study for exam. Thanks I will upvote the best and neat answer

Answer 1

Volume of Solid Figures: Given, A frustum of a pyramid with square base of side b and square top of side a below: b We have to find the volume of the given frustum of heighth.

h Pyramid sliced parallel to base frustum b Since the formula for pyramid with square base is given as follows: V = (Base Area)xh = 3 Therefore, the volume of bigger pyramid is equal to the volume of smaller pyramid plus truncated part of bigger pyramid. =V +V Smaller Frushon =V. -V Bigger Smaller V Frustion

Therefore, V. Frusto = n +h")6° -} (a)H' - 3 no +31(63–a) Now, ha h'= b-a Therefore, VE hbº + 1 ha 3 b-a Frust (b-a)(b+a) h(b? +ab+a) Il Hence, the required volume is V = sh(b + ab +a?)|

Case I: Ifa=b, then we get a rectangular prism of height h and for volume put a=b in the above volume formula as follows: V=hl H(b2+b.b+b) 3bh =bh Case II: Ifa=0, then we get a pyramid with square base of height hand for volume put a=0 in the above volume formula as follows: V =h(02+0b+bº) -bh 3 Hence, the required results are obtained.