# Volume of Solids - Page 2

Questions

- The base of a triangular pyramid is a triangle with corners at #(4 ,2 )#, #(3 ,7 )#, and #(5 ,3 )#. If the pyramid has a height of #5 #, 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 #66 # and the height of the cylinder is #5 #. If the volume of the solid is #45 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 that of the cone. The height of the cone is #42 # and the height of the cylinder is #6 #. If the volume of the solid is #60 pi#, what is the area of the base of the cylinder?
- An ellipsoid has radii with lengths of #6 #, #8 #, and #5 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
- Cups A and B are cone shaped and have heights of #25 cm# and #27 cm# and openings with radii of #12 cm# and #12 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 #8 #, and the cap's radius is #8 #. What is the object'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 #42 # and the height of the cylinder is #6 #. If the volume of the solid is #45 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 that of the cone. The height of the cone is #33 # and the height of the cylinder is #4 #. If the volume of the solid is #25 pi#, what is the area of the base of the cylinder?
- A chocolate is made in the shape of a sphere of diameter #4cm#, which has hollow inside of diameter #3.7cm#. What is the volume of the chocolate?
- The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,1 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
- Cups A and B are cone shaped and have heights of #34 cm# and #37 cm# and openings with radii of #12 cm# and #17 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 #66 # and the height of the cylinder is #5 #. If the volume of the solid is #96 pi#, what is the area of the base of the cylinder?
- If the volume of a sphere is #2304pi#, then what is the diameter?
- 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 #21 #. If the volume of the solid is #420 pi#, what is the area of the base of the cylinder?
- The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,5 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
- Ramesh has the following three containers - cylindrical container a,having radius r and height b - cylindrical container b,having radius 2r and height 1/2b - cuboidal container c,having dimensions r*r*b increasing order of V is? The arrangement of
- 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 #12 #. If the volume of the solid is #24 pi#, what is the area of the base of cylinder?
- The base of a triangular pyramid is a triangle with corners at #(5 ,8 )#, #(6 ,7 )#, and #(2 ,3 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?
- An ellipsoid has radii with lengths of #3 #, #3 #, and #8 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
- An ellipsoid has radii with lengths of #6 #, #9 #, and #7 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?