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 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:

$V_1, V_2, V_3$ 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:

Which of the following statements are incorrect?

(a) Volume of a cone = $\frac{1}{3}\pi r^3 h$

(b) Volume of a cone = $\frac{1}{3}\pi r^2 h$

(c) Volume of a hemisphere = $\frac{2}{3}\pi r^2$

(d) Volume of a hemisphere = $\frac{2}{3}\pi r^3$

(e) Volume of a cylinder = $\frac{1}{3}\pi r^3 h$

Choose the correct answer from the options given below:

A sector as shown in the figure is assembled to form a cone. What is the base radius (in cm) of the cone so formed ? $\left(\pi = \frac{22}{7}\right)$

If the diagonal of a cube is $8\sqrt{3}$ cm then the volume of cube is :

A right angle triangle is rotated along the base. If the perpendicular, hypotenuse and base of the triangle are 8 cm, 10 cm and 6 cm respectively. Find the volume of the cone formed through rotation. ($\pi = 3.14$)