Question:

Tim counted 24 mole rats in an exhibit at the zoo. Then he realized that he forgot to count x mole rats.

A. Write an expression to represent the number of mole rats in the exhibit. Why is this the correct expression?

B. Suppose a sign next to the exhibit says that there are 36 mole rats. What is the value of x? Explain your reasoning.

C. Now that you know there are 36 mole rats in the exhibit, write an expression to represent the number of mole rats that Tim counted. Use x in the expression.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)