you bake a dessert in the baking pan shown. you cut the dessert into cube shaped pieces of equal size. each piece has a volume o
f 8cubic inches how many pieces do you get from one pan?
1 answer:
Answer:
16 pieces
Step-by-step explanation:
The complete question in the attached figure
step 1
Find the length side of each cube shaped piece
we know that
The volume of the cube is equal to
where
b is the length side of the cube
we have
so
solve for b
step 2
How many pieces do you get from one pan?
we know that
The height of the dessert in the baking pan is equal to the height of the cube
so
The total volume of the dessert in the baking pan is equal the area of the square base multiplied by the height
Divide the total volume of the dessert by the volume of one cube
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Based on the calculations, the depth of tent is equal to 12 feet.
<h3>How to calculate the depth of the tent?</h3>Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):
- Triangle ABC is an isosceles triangle (AB = AC).
- The front and back of the triangle are identical triangles.
- Side AD is perpendicular side BC.
- CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.
Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:
AC² = AD² + DC²
AD² = AC² - DC²
AD² = 5² - 3²
AD² = 25 - 9
AD² = 16
AD = √16
AD = 4 feet.
Also, we would determine the area of the triangle (ABC):
Area = 1/2 × b × h
<u>Where:</u>
- b is the base area.
- h is the height.
Substituting the given parameters into the formula, we have;
Area = 1/2 × 6 × 4
Area = 12 feet².
Depth of tent = 3 × height of ADC
Depth of tent = 3 × 4
Depth of tent = 12 feet.
Read more on area of triangle here: brainly.com/question/21917592
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