What is the volume of the cone? What is the volume of the cylinder? What is the volume of the sphere? At the craft store discuss
ed above, the clay cone is $12, the clay cylinder is $30, and the clay sphere is $28. Which is the best buy? Explain. Hint: Which shapes gives you more clay for less money?
1 answer:
Answer:
clay sphere gives more clay for less money
Step-by-step explanation:
Volume of cone=1/3πr^2h
=1/3*3.14*(9^2)*12
=1/3*3.14*81*12
=3,052.08/3
=1017.36 inches^3
Volume of a cyclinder=πr^2h
=3.14*(9^2)*12
=3.14*81*12
=3,052.08 inches^3
Volume of a sphere=4/3πr^3
=4/3*3.14*(9^3)
=4/3*3.14*(9^3)
=4/3*3.14*729
=9,156.24 / 3
=3,052.08 inches^3
Clay cone=$12
Clay cyclinder=$30
Clay sphere=$28
Which is the best to buy
Comparing volume
Volume of sphere=3,052.08 inches^3
Volume of cyclinder=3,052.08 inches^3
Volume of cone=1017.36 inches^3
Sphere and cyclinder both have the same volume which is 3 times more than volume of a cone
Clay sphere cost $28 which is cheaper than clay cyclinder at the same volume.
Therefore, clay sphere gives more clay for less money
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Answer:
Step-by-step explanation:
When given the following inequality;
Rewrite in a fractional form so that it is easier to work with. Remember, a ratio is another way of expressing a fraction where the first term is the numerator (value over the fraction) and the second is the denominator(value under the fraction);
Now bring all of the terms to one side so that the other side is just a zero, use the idea of inverse operations to achieve this:
Convert the (1) to have the like denominator as the other term on the left side. Keep in mind, any term over itself is equal to (1);
Perform the operation on the other side distribute the negative sign and combine like terms;
Factor the equation so that one can find the intervales where the inequality is true;
Solve to find the intervales when the equation is true. These intervales are the spaces between the zeros. The zeros of the inequality can be found using the zero product property (which states that any number times zero equals zero), these zeros are as follows;
Therefore the intervales are the following, remember, the denominator cannot be zero, therefore some zeros are not included in the domain
Substitute a value in these intervales to find out if the inequality is positive or negative, if it is positive then the interval is a solution, if it is negative then it is not a solution. This is because the inequality is greater than or equal to zero;
-> negative
-> neagtive
-> neagtive
-> positive
Therefore, the solution to the inequality is the following;