10 Question MCQ (including Assertion)

A cubical ice cream brick of edge \(22\text{ cm}\) is to be distributed among some children by filling ice cream cones of radius \(2\text{ cm}\) and height \(7\text{ cm}\) up to their brim. How many children will get the ice cream cones?

A metallic spherical shell of internal and external diameters \(4\text{ cm}\) and \(8\text{ cm}\), respectively, is melted and recast into a cone of base diameter \(8\text{ cm}\). The height of the cone is:

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

The radii of the top and bottom of a bucket of slant height \(45\text{ cm}\) are \(28\text{ cm}\) and \(7\text{ cm}\), respectively. The curved surface area of the bucket is:

The volumes of two spheres are in the ratio \(64:27\). The ratio of their surface areas is:

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter \(2\text{ cm}\) and height \(16\text{ cm}\). The diameter of each sphere is:

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:

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?

An ice-cream cone of radius \(r\) and height \(h\) is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is \(\frac{r}{2}\), then h : 2r equals