Question : The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm, what is the length of the side of the equilateral triangle?

Option 1: $\frac{22}{3}$ cm

Option 2: $\frac{44}{3}$ cm

Option 3: $44$ cm

Option 4: $22$ cm

Question : The length of the median of an equilateral triangle is $12\sqrt3 \text{ cm}$. Then, the area of the triangle is:

Option 1: $144\text{ cm}^2$

Option 2: $288\sqrt3\text{ cm}^2$

Option 3: $144\sqrt3\text{ cm}^2$

Option 4: $288\text{ cm}^2$

Question : What is the altitude of an equilateral triangle whose side is 15 cm?

Option 1: $15\sqrt3\text{ cm}$

Option 2: $10\sqrt 3\text{ cm}$

Option 3: $\frac{9\sqrt 3 }{2}\text{ cm}$

Option 4: $\frac{15\sqrt 3}{2}\text{ cm}$

Question : In a right-angled triangle $\Delta PQR, PR$ is the hypotenuse of length 20 cm, $\angle PRQ = 30^{\circ}$, the area of the triangle is:

Option 1: $50\sqrt{3}\text{ cm}^{2}$

Option 2: $100\sqrt{3}\text{ cm}^{2}$

Option 3: $25\sqrt{3}\text{ cm}^{2}$

Option 4: $\frac{100}{\sqrt{3}}\text{ cm}^{2}$

Question : If the diameter of a sphere is 7 cm, find the volume of the sphere. (use $\pi=\frac{22}{7}$) (Rounded up to two decimal places).

Option 1: $184 \ \text{cm}^3$

Option 2: $201.34\ \text{cm}^3$

Option 3: $128.87 \ \text{cm}^3$

Option 4: $179.67 \ \text{cm}^3$