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.