Question
A water pipe is a cylinder 30 inches long, with a radius of 1 inch. At one end of the cylinder there is a hemisphere. What is the volume of the water pipe?
Hint:
We simply recall the formulae for volume of both cylinder and hemisphere by putting the common radius as 1 inch and solve the problem.
The correct answer is: The volume of the pipe is 302/3 π cube inches.
Explanations:
Step 1 of 2:
Given, base radius r = 1 inch and height h = 30 inches
The radius of the hemisphere r = 1 inch.
Volume of the cylinder =
Volume of the hemisphere = 
Step 2 of 2:
Volume of the pipe = volume of cylinder + volume of hemisphere
Final Answer:
The volume of the pipe is 
cube inches.
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Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
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Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?
Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.
