Problem:
Anne's bakery offers personalized cakes for children's birthday parties and other special occasions. the bakery once the volume of escape to be 351 cubic inches. the rectangle cake has a length of four inches longer than its width and its height is one-third of its width. what should be the dimension of the cake pan? ​
Given:
V = 351 in³
L = 4 + W
H = (1/3)W
Solution:
V = LWH
351 = (4 + W)(W)(W/3)
351(3) = (4 + W)(W)(W)
1053 = 4W² + W³
W³ + 4W² - 1053 = 0
(W - 9)(W² + 13W + 117) = 0
W = 9
Checking:
L = 4 + W
L = 4 + 9
L = 13 in
H = (1/3)W
H = W/3
H = 9/3
H = 3
V = 351 in³
LWH = 351
13(9)(3) = 351
351 = 351 ; ok
Answer:
The dimension of the cake pan is
L = 13 in
W = 9 in
H = 3 in
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