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?
Answers
Given :- 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.
Solution :-
Let us assume that width of the cake is x inches .
so,
→ Length of cake = (x + 4) inches .
→ Height of cake = (x/3) inches.
then,
→ Volume of cake = Length * width * height .
→ x * (x + 4) * (x/3) = 351
→ x²(x + 4) = 351 * 3
→ x²(x + 4) = 1053
→ x²(x + 4) = 81 * 13
→ x²(x + 4) = 9² * (9 + 4)
therefore,
→ x = 9 inches.
hence,
- Length of cake = (x + 4) = 9 + 4 = 13 inches.
- Width of cake = x = 9 inches .
- Height of cake = (x/3) = 9/3 = 3 inches.
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