Analyze and solve the following word problems.
1. The volume V of a cylinder is expressed by the formula Vrh, where r is the radius of the base and h is the height of the cylinder. A prototype can for packaging has a volume of (x²+2x-24) cu. cm and a radius of (x+6) cm. Write the rational algebraic expression that represents the height of the prototype can in simplest form.
Solution and answer:
1. The volume V of a cylinder is expressed by the formula Vrh, where r is the radius of the base and h is the height of the cylinder. A prototype can for packaging has a volume of (x²+2x-24) cu. cm and a radius of (x+6) cm. Write the rational algebraic expression that represents the height of the prototype can in simplest form.
Solution and answer:
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Word Problem
Volume of cylinder = πr²h
Given:
Volume = x² + 2x - 24
radius = x+6
Solution:
V = r²h
h = V / r²
h = (x² + 2x - 24) / (x + 6)²
x² + 2x - 24 = (x + 6)(x - 4)
h = (x + 6)(x - 4) / (x + 6)²
h = (x - 4) / (x + 6)
Answer:
[tex]h = \frac{x - 4}{x + 6} [/tex]
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