A rectangular sheet 50 cm by 30 cm is rolled along the 30 cm side to form a cylinder (open at both ends). The radius of the cylinder is:

$V_1, V_2, V_3$ and $V_4$ are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4x cm respectively. The following statements regarding these volumes are given below.

(A) $V_1 + V_2 + 2V_3 < V_4$

(B) $V_1 + 3V_2 > V_3 + V_4$

(C) $2(V_1 + V_3) + V_2 = V_4$

(D) $V_1 + 4V_2 + V_3 < V_4$

Which of these statements is/are correct?

Choose the correct answer from the options given below:

Arrange the volumes of the following geometrical figures in decreasing order of their value.

A. A cuboid of length 5 cm, breadth 3 cm and height 4 cm.

B. A cube on each side of 4 cm.

C. A cylinder of radius 3 cm and length 3 cm.

D. A sphere of radius 3 cm.

Choose the correct answer from the options given below:

The heights of two right circular cones are in the ratio 1 : 2 and the circumferences of their bases are in the ratio 3 : 4. Find the ratio of their volumes.

Consider the following statements:

I. If the height of a cylinder is doubled, the area of the curved surface is doubled.

II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

Which of the above statement(s) is / are true:

A right circular cylinder has radius 7 cm and height 10 cm. Another cylinder has twice the height and half the radius. The ratio of their volumes (first : second) is:

A cylindrical jar having a base of radius 15 cm, is filled with water up to a height of 20 cm. If a solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in the water, then the increase in the level of water is: