Areas related to circles - perimeter and area of a circle for class 10 maths.
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Areas related to circles - perimeter and area of a circle for class 10 maths.
- 1. Areas Related To Circles Problems based on Perimeter and area of a circle Chapter : Areas Related To Circles Website: www.letstute.com
- 2. Problems based on Perimeter and area of a circle Q) Find the circumference and area of the circle of radius 7.2cm. Given: Radius of the circle = 7.2cm To Find: a) Circumference of the circle = ? b) Area of the circle = ? O 7.2 cm Chapter : Areas Related To Circles Website: www.letstute.com
- 3. Problems based on Perimeter and area of a circle Solution: Let the radius of the circle be ‘r’ r=7.2cm ---------- (given) a) Circumference = 2πr =2x22x7.2cm 7 = 45.26 cm b) Area = πr2 = 22x7.2x7.2cm2 7 = 162.93 cm2 O 7.2 cm Chapter : Areas Related To Circles Website: www.letstute.com
- 4. Problems based on Perimeter and area of a circle Result: a) Circumference= 45.26cm b) Area= 162.93cm2 Hence, the circumference of the circle is and its area is 45.26cm 162.93 cm2 O 7.2 cm Chapter : Areas Related To Circles Website: www.letstute.com
- 5. Problems based on Perimeter and area of a circle Q) The diameter of a watermelon slice is 8cm. Find its perimeter. Given: Diameter = 8cm To Find: Perimeter of the slice = ? 8cm Chapter : Areas Related To Circles Website: www.letstute.com
- 6. Problems based on Perimeter and area of a circle Solution: Let ‘r’ be the radius of the watermelon slice. 8cm r = Diameter = 8cm = 4cm 2 2 Perimeter = 1x 2πr+2r of the slice 2 22 1 4 2 4 2 2 =20.57 cm 7 20.57cm Result: Perimeter of the slice = 20.57 cm Hence, the perimeter of the watermelon slice is Chapter : Areas Related To Circles Website: www.letstute.com
- 7. Problems based on Perimeter and area of a circle Q) The difference between the circumference and diameter of a wheel is 18cm. Find the radius of the wheel. Given: Circumference - diameter=18cm To Find: Radius of the wheel = ? O ? cm Chapter : Areas Related To Circles Website: www.letstute.com
- 8. Problems based on Perimeter and area of a circle Solution: Let the radius of the wheel be ‘r’ Circumference-Diameter = 18cm ------- (Given) 2πr-2r = 18cm 2r(π-1) = 18cm 2r 1 = 18cm 2r = 18cm 2r x 15 = 18cm 22 7 7 7 r = 18x7 cm 2x15 22 7 O ? cm Chapter : Areas Related To Circles Website: www.letstute.com
- 9. Perimeter and area of a circle = 9x7 cm 15 = 3x7 cm 5 = 21 cm 5 = 4.2cm Problems based on Result: Radius of the wheel= 4.2cm Hence, the radius of the wheel is 4.2cm O ? cm Chapter : Areas Related To Circles Website: www.letstute.com
- 10. Problems based on Perimeter and area of a circle Q) A wire is in the form of a circle of radius 50cm. It is bent into a square. Determine the side of the square. O Before Given : Radius of the circle = 50 cm To Find: Side of the square = ? Chapter : Areas Related To Circles Website: www.letstute.com
- 11. Problems based on Perimeter and area of a circle Solution: Let the radius of the circle be ‘r’ r = 50cm ---------- (given) Length of the wire = Circumference of the circle = 2πr = 2x22x50cm 7 = 2200 cm 7 = 314.28cm O Before Chapter : Areas Related To Circles Website: www.letstute.com
- 12. Problems based on Perimeter and area of a circle Let ‘x’ be the side of the square. Perimeter of the square = Length of the wire (circumference) 4x = 314.28 x = 314.28 4 x = 78.57 cm X cm After Hence, the side of the square is 78.57cm Chapter : Areas Related To Circles Website: www.letstute.com
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Editor's Notes
- A very good day to all of you’ll out there…… before we move on to the first question, lets put on our thinking caps as we tackle some problems. Moving on to the first question, Find the circumference and area of the circle of radius 7.2cm. We have been given that the radius of the circle is 7.2 cm. We need to find 2 things, a) Circumference of the circle b) Radius of the circle
- So, ;let us see the solution….. Firstly let us represent the radius of the circle to be r R as we know is 7.2 cm In order to find the circum., we need to use a formula. So, do you’ll remember the formula for circumference??? The formula is = 2πr No by substituting the value of pie by 22/7 and r by 7.2, we get =2x22x7.2cm 7 On firther simplifying this step, we get the answer to be 45.26 cm = 45.26 cm Cuming on to the b part, We are asked to find out the area of the circle, Area is given by the formula = πr2 By substituting pie by 22/7 and r by 7.2, we get = 22x7.2x7.2cm2 7 On further simplificatn we get, = 162.93 cm2
- So, the result is a) a) Circumference= 45.26cm b) Area= 162.93cm2 Hence, the circumference of the circle is 45.26cm and its area is 162.93cm2
- Let us see the next question, The diameter of a watermelon slice is 8cm. Find its perimeter. Let us see what is given to us, We have Diameter which is 8 cm What we need to find is the perimeter of the slice.
- Moving on to the solution, Lets us denote radius of the watermelon slice as r We have been given diameter of the slice which is 8 cm. In order to find the radius, we have a formula. Radius = diameter = 8 = 4 2 2 What we now need to find out is the perimeter of the slice. The perimeter can be determibned by the formula 1x 2πr+2r 2 By substituting pie by 22/7 and r by 4, we get ½ x 2 x 22/7 x 4 + 2 x 4 By cancelling out 2, and further simplificatn, we gt, The answer to b 20.57 cm Thus, Hence, the perimeter of the watermelon slice is 20.57 cm
- Let us now tackle the next questn which says that The difference between the circumference and diameter of a wheel is 18cm. Find the radius of the circle. Firstly, let us see what is given to us. We hve, Circumference - diameter=18cm What we need to find is the radius.
- Solution = Let r be the radius of the circle. We have been given Circumference-Diameter = 18cm ------- (Given) We already know the formula for the circumference of the circle. And that of diameter which is 2r By using the respective formulas, we get, 2πr-2r = 18cm By taking 2r common, we get 2r(π-1) = 18cm, now by substituting pie by 22/7, we get, 2r( 22/7 -1) = 18cm On cross multiplication, we get, 2r(22-7 /7) = 18cm On subtracting, 22 by 7, we get 15, thus the next step will be 2r x 15 = 18cm 7 As we need to determine the radius of the wheel, we need to isolate r by taking all d values on the RHS, so we get, r = 18x7 cm 2x15 On further simplificatn, we get,
- , Thus, the result is the radius of the circle is 4.2 cm
- The next questn is A wire is in the form of a circle of radius 50cm. It is bent into a square. Determine the side of the square. Lets see what is given to us, we have the radius of the circle which is 50 cm. The circle is then bent into a sqaure. What we need to determine is the side of the square after it has been bent.
- Let us take a look at the solution, Firstly, let us represent the radius of the circle as r, Thus, r = 50 cm which is given to us. We all know that the length of the square is equal to the circumference of the circle. The circumference of the circle is given by the formula, 2πr by substituting pie by 22/7 and r by 50, we get = 2x22x50cm 7 By multiplyin 2x22x50, we get, =2200 7 On further division, we get = 314.28cm
- Now, the wire which is in the form of a circle is bent into a square, So, let us consider the side of the square to b ‘x’ Now, the Perimeter of the square = Length of the wire which is the (circumference) The perimeter of the square is given by the formula 4x and we already found out the cicumference , thus we get, 4x = 314.28 as we need to find out the value of x, we need to isolate it by taking 4 to the RHS, thus we get, x = 314.28 4 On division, we get x = 78.57 cm Thus, the side of the square is 78.57 cm