Question

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
v=(2a+11)(5a-12)(a+6)
v=(10a^2-24a+55a-132)(a+6)
v=(10a^3+60a^2-24a^2-144a+55a^2+330a-132a-792
v=10a^3+60a^2-24a^2+55a^2-144a+330a-132a-792
v=10^3+91a^2+54a-792

Answer 1

 For this case the volume of the box is given by:
 $V = lwh$
 Substituting values we have:
 $V = (2a + 11) (5a - 12) (a + 6)$
 Rewriting we have:
 $V = (10a ^ 2-24a + 55a-132) (a + 6) V = 10a ^ 3-24a ^ 2 + 55a ^ 2-132a + 60a ^ 2-144a + 330a-792$
 Grouping terms of equal degree we have:
 $V = 10a ^ 3 + 60a ^ 2 -24a ^ 2 + 55a ^ 2 -132a -144a + 330a-792$
 Adding terms of equal degree we have:
 $V = 10 ^ 3 + 91a ^ 2 + 54a-792$
 Answer:
 the volume of the box is:
 All the expressions given.