Advertisements
Advertisements
प्रश्न
ABC is an isosceles right-angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. [Take π = 22/7]
उत्तर
In ΔABC, using Pythagoras theorem
AC2 = AB2 + BC2
AC2 = (7)2 + (7)2
AC2 = 49 + 49
AC2 = 98
⇒ AC = `7sqrt2`
Radius of semi-circle = `"AC"/2 = (7sqrt2)/2`
∴ Area of the shaded region = Area of semi-circle – Area of ΔABC
Area of semi-circle = `1/2 pir^2 = 1/2 pi((7sqrt2)/2)^2`
= `(98pi)/8 = (49pi)/4`
= `49/4`
= `49/4 xx 22/7`
= `77/2 "cm"^2`
Area of ΔABC = `1/2` x BC x AB
= `1/2` x 7 x 7
= `49/2 "cm"^2 `
Thus, Area of the shaded region = `77/2 "cm"^2 - 49/2 "cm"^2 = 28/2 "cm"^2 = 14 "cm"^2`.
APPEARS IN
संबंधित प्रश्न
In Fig. 2, a circle is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.
In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use `pi=22/7`]
If the perimeter of a semi-circular protractor is 66 cm, find the diameter of the protractor (Take π = 22/7).
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
A playground has the shape of rectangle, with two semicircles on its smaller sides as diameters, added to its outside. If the sides of rectangle are 36m and 24.5m. find the area of playground.
The area of a circle is 49 π cm2. Its circumference is:
The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm2 Find the radii of the two circles.
The speed of the car is 66 km/hour. If each wheel of the car is 140 cm in diameter, find the number of revolutions made by each wheel per minute.
Find the total surface area and volume of a hemisphere whose radius is 10 cm.
There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.
The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = `22/7`)
Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radius 15 cm and 8 cm.
Find the perimeter of the given shape (Take π = `22/7`).
The diameter of the bullock cart wheel is 1.4 m. Find the distance covered by it in 150 rotations?
A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m2.
Circumference of a circle of diameter 5 cm is ______.
The distance around a circle is its ______.
Find the total cost of wooden fencing around a circular garden of diameter 28 m, if 1 m of fencing costs ₹ 300.
The circumferences of two circles are in the ratio 4 : 5. What is the ratio of their radii?
