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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

Verified Answer :

carlosego

 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.

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