8) A school community had planned to reduce the number of grade 9 students per class room by constructing additional class rooms. However, they constructed 4 less rooms than they planned. As the result, the number of students per class 10 more than they planned. If there are 1200 grade nine students in the school, determine the current number of class rooms and the number of students per class.

Step-by-step explanation:

Let "c" be the original number of classrooms.

The 1200/c was the original number of students per classroom.

Equation:

1200/(c-4) = (1200/c)+10

Multiply thru by c(c-4)

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1200c = 1200(c-4)+10c(c-4)

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1200c = 1200c-4800 + 10c^2-40c

10c^2-40c-4800 = 0

c^2-4c-480 = 0

Factor:

(c-24)(c+20) = 0

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Positive solution:

c = 24 (# of classrooms originaly planned)

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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