You must be logged in to see worked solutions.

Already have an account? Log in here.

What is the volume of a sphere of radius 5? If we make a cylinder two times taller, and its radius three times bigger, how many times larger would it become in volume? See more

If the above diagram consists of a semi-sphere and a circular cone with \(r=9\text{ cm}\) and \(h=9\text{ cm},\) what is its volume?

The above diagram is not drawn to scale.

You must be logged in to see worked solutions.

Already have an account? Log in here.

\(18\) rigid balls of radius \(4\text{ cm}\) are closely packed in a rectangular cuboid, as shown above. What is the ratio between the total volume occupied by the \(18\) balls and the volume of the rectangular cuboid?

You must be logged in to see worked solutions.

Already have an account? Log in here.

The cylinder on the left is filled with water, and the radius and height of the cylinder are \(r=3\text{ cm}\) and \(h=10\text{ cm},\) respectively. Now, we insert a rigid sphere with radius \(3\text{ cm}\) into the cylinder causing the water to spill over. If all the water overflowing from the left cylinder can be contained in the right cylinder with radius \(3\text{ cm},\) what is the minimum value of the height \(H\) of the right cylinder in \(\text{cm} ?\)

You must be logged in to see worked solutions.

Already have an account? Log in here.

The above diagram is a right pyramid with the following lengths:
\[\begin{align}
{\overline{AB}} &= {\overline{BC}} = {\overline{CD}} = {\overline{AD}} =4, \\
{\overline{OA}} &= {\overline{OB}} = {\overline{OC}} = {\overline{OD}} =2\sqrt{6}.
\end{align} \]
What is the volume of this pyramid?

You must be logged in to see worked solutions.

Already have an account? Log in here.

Quadrilateral \(ABCD\) is a square with side length \(18\text{ cm},\) and \(E\) and \(F\) are the midpoints of \(\overline{BC}\) and \(\overline{CD},\) respectively. If we fold up the three corners \(B,\) \(C\) and \(D\) to make a polyhedron, then what is the volume of the polyhedron in \(\text{cm}^3 ?\)

You must be logged in to see worked solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...