A new bakery offers decorated cakes for birthdays and special occasions. The cak...

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12085141 @12085141

October 2022 1 0 Report

A new bakery offers decorated cakes for birthdays and special occasions. The cake is in

the shape of a rectangular solid whose length is 4 inches longer than the width and the

height is 3 inches. What should be the dimensions of the cake pan if the volume of the cake

is 180 cubic inches? (Hint: Use V = lwh, set x = width, refer to the figure below)

Answers & Comments

KAntoineDoix

Verified answer

VOLUME

==============================

Solve:

$\implies \large \sf{V = lwh}$

$\sf let \: x \: be \: the \: width \: (or \: w)\\ \large \tt \red{given} \begin{cases} \sf \: l = 4 + x \\ \sf \: h = 3 \\ \sf \: V = 180 \end{cases} \\ \\$

$\implies \large \sf{180 = (4 + x)x( 3)}$

$\implies \large \sf{180 = (4 + x)3x}$

$\implies \large \sf{180 = (12x + {3x}^{2} )}$

$\:$

Following the standard form, rearrange the terms by transposing then factor the equation

$\implies \large \sf - 3 {x}^{2} - 12x + 180 = 0$

$\implies \large \sf \frac{ - 3 {x}^{2} - 12x + 180}{ - 3} = 0 \\$

$\implies \large \sf {x}^{2} + 4x - 60 = 0$

$\implies \large \sf (x + 10)(x - 6) = 0$

$\large \sf (x + 10) = 0 \: \: \:, \: \: (x - 6) = 0 \\ \orange{ \sf \large x = - 10 \: \: \:, \: \: x = 6 \: \: \: \:} \\ \\$

Length is always longer than the width, and there should be no negative length. Follow the rules.

$\implies \sf \large l = 10$

$\implies \sf \large x = 6$

$\:$

Final Answer:

$\large \implies \sf \orange{10 \: in. \: was \: the \: length}$

$\large \implies \sf \orange{6 \: in. \: was \: the \: width}$

$\large \implies \sf \orange{3 \: in. \: was \: the \: heigth}$

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VOLUME

==============================

Solve:

Final Answer:

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