The angle of a sector is π/4 radians, and the radius of the circle is 8 cm. What is the area of the sector?
8π cm^2
The area of a sector is given by \(\text{Area} = \frac{1}{2}r^2\theta\), where θ is in radians.
Substituting \(r=8\) and \(\theta = \frac{\pi}{4}\): \(\text{Area} = \frac{1}{2}(8)^2 \times \frac{\pi}{4} = \frac{1}{2} \times 64 \times \frac{\pi}{4}\).
Calculating, \(\frac{1}{2} \times 64 \times \frac{\pi}{4} = \frac{64\pi}{8} = 8\pi\).
Hence, the answer is 8π cm².
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Important Questions from Mensuration
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
