Question : The base of a right pyramid is an equilateral triangle with a side of 8 cm, and its height is $30 \sqrt{3}$ cm. The volume (in cm$^3$ ) of the pyramid is:

Option 1: $240 \sqrt{3}$

Option 2: $360 \sqrt{3}$

Option 3: $480$

Option 4: $360$

Question : A pyramid has an equilateral triangle as its base, of which each side is 8 cm. Its slant edge is 24 cm. The whole surface area of the pyramid (in cm²) is:

Option 1: $(16 \sqrt{3}+24 \sqrt{35})$

Option 2: $(12 \sqrt{3}+24 \sqrt{35})$

Option 3: $(24\sqrt{3}+36\sqrt{35})$

Option 4: $(16\sqrt{3}+48\sqrt{35})$

Question : The base of a right pyramid is a square of side $8 \sqrt{2}$ cm and each of its slant edges is of length 10 cm. What is the volume (in cm$^3$) of the pyramid?

Option 1: $256$

Option 2: $224$

Option 3: $426 \frac{2}{3}$

Option 4: $96 \sqrt{2}$

Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.

Option 1: $5 \sqrt{3}~cm$

Option 2: $3 \sqrt{3}~cm$

Option 3: $\frac{1}{\sqrt{3}}~cm$

Option 4: $\frac{5}{\sqrt{3}}~cm$

Question : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?

Option 1: $2\sqrt{3}$ cm

Option 2: $5\sqrt{3}$ cm

Option 3: $4\sqrt{3}$ cm

Option 4: $3\sqrt{3}$ cm