Question

"A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the volume of a small cake to be 351 cubic inches. The cake is in the shape of a rectangular solid. They want the length of the cake to be four inches longer than the width of the cake and the height of the cake to be one-third of the width. What should the dimensions of the cake pan be?"

Answer 1

Answer:

$w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}$      

Step-by-step explanation:

We are given the following in the question:

Volume of cake = 351 cubic inches

Let x inches be the width of cake.

Width of cake, w =

$x\text{ inches}$

Then, length of cake,l =

$(x + 4)\text{ inches}$

Height of cake,h =

$\dfrac{x}{3}\text{ inches}$

Volume of cake = Volume of cuboid

$V = lwh$

Putting values, we get:

$351 = x(x+4)(\dfrac{x}{3})\\\\1053 = x^3 + 4x\\x^3+4x^2-1053= 0\\\\\text{For x = 9}\\(9)^3+4(9)^2-1053= 0$

Thus, dimensions of cake are:

$w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}$