A volume of a wall is 128 cm$^3$. If the height of the wall is 6 times its breadth and the length is 9 times its breadth, find the breadth.

Consider the volumes of the following:

(A) A cylinder with a radius of base 7 cm and height 10 cm.

(B) A cone of radius 7 cm and height 9 cm.

(C) A sphere of radius 6 cm.

The volumes of these figures in decreasing order shall be:

Choose the correct answer from the options given below:

$V_1, V_2, V_3$ 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:

The solid and the Surface area (S.A) of the following solids are given below.

(A) A cube of edge 9 cm., S.A = $486 \text{ cm}^2$

(B) A cuboid of 18 cm. long, 14 cm. width and 7 cm. height, S.A = $108 \text{ cm}^2$

(C) A cylinder with diameter of 14 cm. and height 80 cm., S.A = $3520 \text{ cm}^2$

(D) A sphere with radius of 14 cm., S.A = $2004 \text{ cm}^2$

Choose the correct answer from the options given below:

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:

In a swimming pool measuring 80 m x 60 m, 120 men take a dip. If the average displacement of water by a man is 6 m$^3$, then the rise in water level is -

From a solid cylinder whose height is 2.4 cm and diameter is 1.4 cm, a conical cavity of same height and same diameter is carved out. The total surface area of the remaining solid is:

Use $\pi = \frac{22}{7}$