The answer is: " 2 in. ".
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Explanation:
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Assume the shape is a "rectangular prism".
Volume of a "rectangular prism" : V = L w h ;
in which:
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V = volume;
L = length;
w = width;
h = height.
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We want to solve for "h" (the "height").
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Given:
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V = 252 in.³ ;
L = 12 in. ;
w = 10.5 in.
Solve for "h" ;
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Plug our "given values" into the formula:
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V = L w h ;
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We want to rewrite this formula/ equation; by isolating "h" (the "height") on on ONE side of the equation;
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Divide EACH SIDE of the formula/equation by "(L w)" ;
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→ V / (L w) = (L w h) / (L w) ;
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to get:
→ V / (L w) = h ;
↔ h = V / (L w) ;
→ h = 252 in.³ / (12 in. 10.5 in.) ;
→ h = 252 in.³ / (126 in.²) ;
→ h = (252 / 126) in. ;
→ h = 2 in.
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The answer is: 2 in.
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