A building is 21 meters high, 15 meters long, and 14+30X meters wide.
Express its volume in terms of X.
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A building is 21 meters high, 15 meters long, and 14+30X meters wide.
Express its volume in terms of X.
We use a formula to calculate the volume: height times width times length.
We rewrite the exercise using the existing data:
We use the distributive property to simplify the parentheses.
We multiply 21 by each of the terms in parentheses:
We solve the multiplication exercise in parentheses:
We use the distributive property again.
We multiply 15 by each of the terms in parentheses:
We solve each of the exercises in parentheses to find the volume:
\( 140-70= \)
Volume measures the space inside a 3D shape. To fill that space, you need length × width × height. Think of it as stacking unit cubes - you need all three directions!
Use distributive property when you have parentheses with addition or subtraction inside. Here, multiply 21 by both terms: and .
X is a variable representing an unknown measurement that affects the building's width. The width changes based on X's value, making the volume depend on X.
Your answer should have two terms: a constant (4410) and a term with X (9450X). Check by substituting a simple value like X=0 or X=1 into your expression.
Since all dimensions are in meters, volume is in cubic meters (m³). When you multiply three lengths together, you get cubic units - that's how volume is always measured!
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