# Volume of Solids - Page 6

Questions

- The base of a triangular pyramid is a triangle with corners at #(1 ,4 )#, #(6 ,2 )#, and #(8 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #5 #. If the volume of the solid is #24 pi#, what is the area of the base of the cylinder?
- A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is #3 # and the height of the cylinder is #5 #. If the volume of the solid is #20 pi#, what is the area of the base of cylinder?
- The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(2 ,7 )#, and #(3 ,6 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
- The base of a triangular pyramid is a triangle with corners at #(7 ,5 )#, #(6 ,9 )#, and #(3 ,8 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?
- An ellipsoid has radii with lengths of #12 #, #7 #, and #7 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #18 # and the height of the cylinder is #1 #. If the volume of the solid is #49 pi#, what is the area of the base of the cylinder?
- The base of a triangular pyramid is a triangle with corners at #(6 ,8 )#, #(2 ,7 )#, and #(7 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?
- Cups A and B are cone shaped and have heights of #16 cm# and #12 cm# and openings with radii of #6 cm# and #8 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the lengths of the top. The prism's height is # 7 #, the cap's height is #4 #, and the cap's radius is #8 #. What is the object's volume?
- Cups A and B are cone shaped and have heights of #27 cm# and #24 cm# and openings with radii of #7 cm# and #9 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #9 # and the height of the cylinder is #6 #. If the volume of the solid is #130 pi#, what is the area of the base of the cylinder?
- A ring torus is made by joining the circular ends of 1 meter long thin and elastic tube. If the radius of the cross section is 3.18 cm, how do you prove that the volume of the torus is #19961# cc?
- The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(1 ,7 )#, and #(5 ,4 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #12 # and the height of the cylinder is #28 #. If the volume of the solid is #36 pi#, what is the area of the base of the cylinder?
- The base of a triangular pyramid is a triangle with corners at #(6 ,4 )#, #(2 ,1 )#, and #(3 ,2 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
- The base of a triangular pyramid is a triangle with corners at #(3 ,2 )#, #(5 ,6 )#, and #(2 ,8 )#. If the pyramid has a height of #9 #, what is the pyramid's volume?
- The base of a triangular pyramid is a triangle with corners at #(3 ,4 )#, #(6 ,2 )#, and #(5 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #13 #. If the volume of the solid is #232 pi#, what is the area of the base of the cylinder?
- The base of a triangular pyramid is a triangle with corners at #(5 ,1 )#, #(2 ,3 )#, and #(9 ,4 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?