Question
The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?
- 11
- 22
- 44
- 66
Hint:
Hint:- The volume of a 3 -dimensional solid is the amount of space it occupies.
The volume V of a cylinder with radius r is the area of the base B times the height h .
V = Bh or V= πr2h
The correct answer is: 44
Solution:-
- We have given volume of a right circular cylinder(A), V1 = 22 cm3
- Let R be radius of cylinder A and H be the height.
- Let the second cylinder denoted as cylinder B
- We have to find the volume of the cylinder B whose radius is twice of cylinder A
Let the radius of cylinder B be R2.
So, R2 = 2R ---------(1)
- Height of cylinder B is half of height of cylinder A.
So, H2 = H/2 ---------(2)
- To find the volume of cylinder B we will have to compare the volumes of both cylinders. Let’s find equation of volume .
- We know the volume of cylinder= πr2h
- Volume of cylinder A = πR2H ----------(3)
- Volume of cylinder B = πR22H2
- Substitute the values of R2 and H2 from equation (1) and (2) in Volume of cylinder B formula.
Volume of cylinder B = π(2R)2(H/2)
= π (4R2)(H/2)
= π (2R2)(H)
Volume of cylinder B = 2πR2H ---------(4)
- Divide the volume of cylinder A by volume of cylinder B from equation (3) and (4).
Volume of cylinder A/ Volume of cylinder B = πR2H / 2πR2H
Volume of cylinder A/ Volume of cylinder B = 1/ 2
- We know the volume of cylinder A is 22 cm3.
So, 22 / Volume of cylinder B = 1/ 2
- Reciprocating both sides we get,
Volume of cylinder B / 22 = 2
- Multiplying both sides by 22 we get,
Volume of cylinder B = 44 cm3
- Therefore, the volume of second cylinder is option C) 44 .
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I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
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For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.
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A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?
I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
In mathematics, a survey is a technique for gathering data that involves posing a series of questions to participants to learn more about their attitudes and behaviors. It is the most typical and affordable method of data collection.
For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.
Types of Survey Methods
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Online Survey
Paper Survey
Telephonic Survey
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