Question

Q. In the given figure ABPC is a quadrant of a circle of radius 14 cm and a semicircle drawn with BC as diameter. Find the area of the shaded region.
Q. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes. If 8 cm of standing water is needed?
Q. A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid after the cone is carved out.

Answer 1

sorry do not know the answer

Answer 2

Ans.1. Area of shaded region = area of semicircle of diameter BC - {area of quadrant of radius AB /AC - area of ∆ABC }

So, area of semicircle of diameter BC = 1/2 πr²

= 1/2 × 22/7 × 7√2 × 7√2 [ ∵ BC is hypotenuse of right angle ∆ABC , here AB = BC = 14 so, BC = 14√2 = 2 × radius ⇒ radius = 7√2 ]

= 11 × 7 × 2 = 154 cm²

area of quadrant of radius AB/AC = 1/4 πr²

= 1/4 × 22/7 × 14 × 14

= 22 × 7 = 154 cm²

area of ∆ABC = 1/2 height × base

= 1/2 × 14 × 14 = 98 cm²

Now, area of shaded region = 154cm² - { 154cm² - 98cm²} = 98cm²

Hence, area of shaded region = 98 cm².

Ans.2. Speed of flowing of water from canal is 10km/h , means length of water flows in 1 hour = 5 km , so length of water flows in 30 minutes = 5km

Now, volume of water flowing from canal = length of water flows in 30 minutes × breadth of canal × deep of canal

= 5000m × 6m × 1.5m = 45000 m³

Let area of field = x m²

Then, volume of water irrigates into the field = area of field × height of water during irrigation

= x m² × 8× 10⁻² m = 0.08x m³

Now, volume of water flowing from canal = volume of water in field

45000 m³ = 0.08x m³

x = 562500 m²

We know, 1 hectare = 10000 m²

So, area of field in hectare = 562500/10000 = 56.25 hectares.

Ans.3. The cone will have a diameter of 14 cm and height of 14 cm. (Radius = 7cm)

Slant height of cone = √(14² + 7²) = 15.652 cm

Surface area = 22/7 x 7 x 15.652 + 22/7 x 7² = 498.35 cm²

Surface area of solid remaining solid = Total surface area of the cube - area of circle where the cone was carved out + curved surface area of cone (hole remaining in the cube)

= 14x14x6 - 22/7x7² + 22/7x7x15.652

= 1366.344 cm²

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