Question : A 64 cm wide path is made around a circular garden having a diameter of 10 metres. The area (in m²) of the path is closest to: (Take $\pi=\frac{22}{7}$)

Option 1: 10

Option 2: 21

Option 3: 15

Option 4: 9

Question : The area (in m²) of a circular path of uniform width $x$ metres surrounding a circular region of diameter d metres is _____.

Option 1: $\pi x(x+2 \mathrm{~d})$

Option 2: $\pi x(x+\mathrm{d})$

Option 3: $\pi x(2 x+\mathrm{d})$

Option 4: $\pi x\left(x+\frac{\mathrm{d}}{2}\right)$

Question : The diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in cm²) of the hemisphere.

Option 1: $25 \pi$

Option 2: $\frac{75 \pi}{4}$

Option 3: $\frac{50 \pi}{4}$

Option 4: $\frac{25 \pi}{4}$

Question : What will be the difference between the total surface area and the curved surface area of a hemisphere having a 4 cm diameter in cm²?

Option 1: $5\pi $

Option 2: $8\pi $

Option 3: $4\pi $

Option 4: $4.4\pi $

Question : The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm³?

Option 1: $192 \pi$

Option 2: $210 \pi$

Option 3: $240 \pi$

Option 4: $180\pi$