Use your calculator to find the combined area of the shaded regions in the figure for different values of the radius r. What is the least whole–number value of r for which the combined area of the shaded regions is greater than 100 square units?
In the figure, the sphere fits perfectly in the cube; that is, it touches each face exactly in the center point of the face.
Assume the sphere has radius r. Use your calculator to find the volume of the region inside the cube but outside the sphere for different values of r. What is the least whole–number value of r for which the volume of this region is greater than 100 cubic units?
Using the GEOBOARD application on your calculator, draw the trapezoid with vertices at (0, 2), (0, 4), (8, 0), and (8, 8).
Use the calculator to find the area of the trapezoid you drew in part a.
Verify the calculator's result from part b by using the formula for the area of a trapezoid.
Using the GEOBOARD application on your calculator, draw the parallelogram with vertices at (0, 2), (5, 2), (8, 7), and (3, 7).
Use the calculator to find the area of the parallelogram you drew in part a.
Verify the calculator's result from part b by using the formula for the area of a parallelogram.
Using the GEOBOARD application on your calculator, draw the kite with vertices at (4, 0), (1, 5), (4, 7), and (7, 5).
Use the calculator to find the area of the kite you drew in part a.
The kite from part a is made up of 4 right triangles. Verify the calculator's result from part b by using the formula for the area of a triangle.
One cylinder has a height of 7 cm and an unknown base radius r. The other has a height of 3 cm and a base radius 2 cm greater than r.
Enter the formulas for the volumes of the two cylinders in your calculator. Find the value of r for which the two volumes are equal, to the nearest tenth.
A right regular pyramid has a square base with side length 2x cm and slant height 1 cm. It encloses a right cone with base radius x.
Use your calculator to find the lateral surface areas of the pyramid and the cone for different values of x. What is the ratio between the two lateral surface areas?
Use the same pyramid and cone from part a. Find the total surface area of the pyramid and the cone for different values of x. Find the ratio between the two total surface areas. What do you notice?
A rectangular carton of orange juice has dimensions 14.2 cm 13.8 cm 12.5 cm. A cylindrical bottle of orange juice from another company holds one half gallon. If both are the same price and quality, which one should you buy?
Oscar's apple farm in Washington State is rectangular in shape, with dimensions 300 yd 120 yd.
Find the area of his farm in acres.
North of the Canadian border, they use the metric system. One hectare (ha) is equal to 10,000 square meters.
Susie's apple farm in British Columbia is circular is shape, with a radius of 105 meters. Find the area of her farm in hectares.
Whose apple farm is bigger, Oscar's or Susie's?
A doctor's syringe holds a cylindrical volume of fluid. The cylinder has a base radius of 1/4 inch and a length of 3 inches. Use your calculator to find out how much fluid is held in the syringe in cubic centimeters.
