Question : There is a wooden sphere of radius $6 \sqrt{3}$ cm. The surface area of the largest possible cube cut out from the sphere will be:

Option 1: $864$ cm²

Option 2: $464 \sqrt{3}$ cm²

Option 3: $462$ cm²

Option 4: $646\sqrt{3}$ cm²

Question : What is the perimeter of a square inscribed in a circle of radius 5 cm?

Option 1: $20 \sqrt{2}\ \mathrm{~cm}$

Option 2: $40\sqrt{2}\ \mathrm{~cm}$

Option 3: $30\sqrt{2}\ \mathrm{~cm}$

Option 4: $10\sqrt{2}\ \mathrm{~cm}$

Question : The base of a right prism is an equilateral triangle whose side is 10 cm. If the height of this prism is $10 \sqrt{3}$ cm, then what is the total surface area of the prism?

Option 1: $125 \sqrt{3}$ cm²

Option 2: $325 \sqrt{3}$ cm²

Option 3: $150 \sqrt{3}$ cm²

Option 4: $350 \sqrt{3}$ cm²

Question : The area of a sector of a circle is 308 cm², with the central angle measuring 45°. The radius of the circle is:

Option 1: 14 cm

Option 2: 21 cm

Option 3: 7 cm

Option 4: 28 cm

Question : ABC is an equilateral triangle with a side of 12 cm. What is the length of the radius of the circle inscribed in it?

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

Option 2: $8 \sqrt{3}$ cm

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

Option 4: $6 \sqrt{3}$ cm