Short Quiz

A container with a grey hemispherical lid has radius R cm . In figure 1, it contains water upto a height of \(\mathbf{R} \mathbf{~ c m}\). It is then inverted as shown in figure 2.

What is the height of water in figure 2?

A cone of maximum size is carved out from a solid cube of edge length \(l\). The volume of the cone is :

Figure 1 below is a solid cuboid made of unit cubes. Figure 2 is obtained after removing some unit cubes from figure 1.
Based on the figures shown above, the surface area of the cuboid in Figure 1 is
\(\_\_\_\_\) the surface area of the solid in Figure 2.

A medicine capsule is in the shape of a cylinder of diameter \(0.5\text{ cm}\), with two hemispheres stuck to its ends. The length of the entire capsule is \(2\text{ cm}\). The capacity of the capsule is: