Question : The base of a right pyramid is an equilateral triangle, each side of which is 20 cm. Each slant edge is 30 cm. The vertical height (in cm) of the pyramid is:

Option 1: $10 \sqrt{\frac{23}{3}}$

Option 2: $5 \sqrt{3}$

Option 3: $10 \sqrt{3}$

Option 4: $5 \sqrt{\frac{23}{3}}$

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 : In a circle of radius 3 cm, two chords of length 2 cm and 3 cm lie on the same side of a diameter. What is the perpendicular distance between the two chords?

Option 1: $\frac{4 \sqrt{3}-3 \sqrt{2}}{2}$ cm

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

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

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

Question : The length of each side of a triangle is 12 cm. What is the length of the circumradius of the triangle?

Option 1: $8 \sqrt{3} \mathrm{~cm}$

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

Option 3: $6 \sqrt{3} \mathrm{~cm}$

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