# Volume of Solids

Understanding the volume of solids is fundamental in various fields, from engineering to mathematics. It encompasses the measurement of space occupied by three-dimensional objects, providing crucial insights into their properties and behaviors. Whether calculating the capacity of a container, analyzing structural integrity, or determining material requirements for manufacturing, a precise grasp of solid volume is indispensable. By exploring geometric principles and mathematical formulas, one can accurately quantify the volume of diverse solids, facilitating efficient design, analysis, and problem-solving in numerous practical applications.

Questions

- The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(5 ,1 )#, and #(7 ,4 )#. If the pyramid has a height of #12 #, 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 #15 # and the height of the cylinder is #4 #. If the volume of the solid is #18 pi#, what is the area of the base of the cylinder?
- Cups A and B are cone shaped and have heights of #33 cm# and #37 cm# and openings with radii of #10 cm# and #7 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?
- Cups A and B are cone shaped and have heights of #39 cm# and #22 cm# and openings with radii of #17 cm# and #13 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 ellipsoid has radii with lengths of #3 #, #4 #, and #7 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
- The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(3 ,1 )#, and #(5 ,9 )#. 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 #12 cm# and #15 cm# and openings with radii of #6 cm# and #4 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 #12 #. If the volume of the solid is #45 pi#, what is the area of the base of the cylinder?
- The base of a triangular pyramid is a triangle with corners at #(2 ,2 )#, #(3 ,1 )#, and #(7 ,3 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?
- Cups A and B are cone shaped and have heights of #35 cm# and #23 cm# and openings with radii of #14 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?
- An ellipsoid has radii with lengths of #6 #, #9 #, and #4 #. 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 #21 pi#, what is the area of the base of the cylinder?
- An ellipsoid has radii with lengths of #15 #, #12 #, and #9 #. A portion the size of a hemisphere with a radius of #7 # 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 #36 # and the height of the cylinder is #8 #. If the volume of the solid is #48 pi#, what is the area of the base of the cylinder?
- How do you find the volume of a sphere with a diameter of 2 inches?
- The side length cube is #3.78 times 10^3# ft. What is the volume of the cube?
- 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 #10 #. If the volume of the solid is #144 pi#, what is the area of the base of the cylinder?
- If the volume of a sphere doubles, what is the ratio of the surface area of the new, larger sphere to the old?
- The image below displays that the water leakage happens from the bottom of the trough at a constant rate. 2hrs later, the level of the water has fallen by 20cm. How many more mins will it take for the trough to empty completely?
- Cups A and B are cone shaped and have heights of #27 cm# and #24 cm# and openings with radii of #7 cm# and #14 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?