What is the volume of the cylinder? Do not round your answer. (Use 3.14 for π .)
1 answer:
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Answer:
Step-by-step explanation:
1. Approach
Since it is given that the garden box is a rectangle, then the opposite sides are congruent. One can use this to their advantage, by setting up an equation that enables them to solve for the width of the rectangle. After doing so, one will multiply the width by the given length and solve for the area.
2. Solve for the width
It is given that the garden box is a rectangle. As per its definition, opposite sides in a rectangle are congruent. The problem gives the length and the perimeter of the rectangle, therefore, one can set up an equation and solve for the width.
Substitute,
Conver the mixed number to an improper fraction. This can be done by multiplying the "number" part of the mixed number by the denominator of the fraction. Then add the result to the numerator.
Inverse operations,
3. Solve for the area
Now that one has solved for the width of the box, one must solve for the area. This can be done by multiplying the length by the width. Since the width is a fraction, one must remember, that when multiplying an integer by a fraction, one will multiply the integer by the numerator (the top of the fraction), and then simplify by reducing the fraction, if possible. Reducing the fraction is when one divides both the numerator and the denominator by the GCF (Greatest Common Factor).
Substitute,
Answer:
(i) 30
(ii) 8
Step-by-step explanation:
Start by drawing 3 rings for the Venn diagram. Each ring represents either Audi, BMW, or Citroën.
Next, add the information provided in the problem statement. We know that 20 choose BMW only. Another 20 choose Citroën only.
We know the number who choose all 3 is the same as the number that choose BMW and Citroën, but not Audi. We'll call this number x.
Similarly, we know that the number who choose all 3 is half of those choose Audi and BMW, but not Citroën. So we'll say that number is 2x.
We know the total number of Audi votes is 48, the total number of BMW votes is 36, and the total number of Citroën votes is 34.
Finally, we know the total number of voters is 100, including those who voted for no favorites (we'll call that number n).
We know that BMW got 36 votes, so:
20 + x + x + 2x = 36
20 + 4x = 36
4x = 16
x = 4
We know that Citroën got 34 votes, so:
20 + x + x + z = 34
20 + 4 + 4 + z = 34
28 + z = 34
z = 6
We know that Audi got 48 votes:
y + 2x + x + z = 48
y + 2(4) + 4 + 6 = 48
y + 18 = 48
y = 30
Finally, we know that the total number of voters is 100.
20 + 20 + x + x + 2x + y + z + n = 100
20 + 20 + 4 + 4 + 2(4) + 30 + 6 + n = 100
92 + n = 100
n = 8
