Maharashtra Board Solutions Class 8-Maths (Practice Set 15.6): Chapter 15- Area

Class 8: Maths Chapter 15 solutions. Complete Class 8 Maths Chapter 15 Notes.

Maharashtra Board Solutions Class 8-Maths (Practice Set 15.6): Chapter 15- Area

Maharashtra Board 8th Maths Chapter 15, Class 8 Maths Chapter 15 solutions

Question 1.
Radii of the circles are given below, find their areas.
i. 28 cm
ii. 10.5 cm
iii. 17.5 cm
Solution:
i. Radius of the circle (r) = 28 cm … [Given]
Area of the circle = πr²
= 227 x (28)²
= 227 x 28 x 28
= 22 x 4 x 28
= 2464 sq. cm

ii. Radius of the circle (r) = 10.5 cm … [Given]
Area of the circle = πr²
= 227 x (10.5)²
= 227 x 10.5 x 10.5
= 22 x 1.5 x 10.5
= 346.5 sq. cm

iii. Radius of the circle (r) = 17.5 cm … [Given]
Area of the circle = πr²
= 227 x(17.5)²
= 227 x 17.5 x 17.5
= 22 x 2.5 x 17.5
= 962.5 sq. cm

Question 2.
Areas of some circles are given below, find their diameters.
i. 176 sq.cm
ii. 394.24 sq. cm
iii. 12474 sq. cm
Solution:
i. Area of the circle =176 sq. cm .. .[Given]
Area of the circle = πr²
∴ 176 = 227 x r²
∴ r² = 176 x 722
∴ r² = 56
∴ r = √56 … [Taking square root of both sides]
Diameter = 2r = 2√56 CM

ii. Area of the circle = 394.24 sq. cm … [Given]
Area of the circle = πr²

∴ Diameter = 2r = 2 x 11.2 = 22.4 cm

iii. Area of the circle = 12474 sq. cm …[Given]
Area of the circle = πr²
∴ 12474 = 227 x r²
∴ r² = 12474 x 722
∴ r² = 567 x 7
∴ r² = 3969
∴ r = 63 …[Taking square root of both sides]
∴ Diameter = 2r = 2 x 63 = 126cm

Question 3.
Diameter of the circular garden is 42 m. There is a 3.5 m wide road around the garden. Find the area of the road.

Solution:

Diameter of the circular garden is 42 m. … [Given]
∴ Radius of the circular garden (r) = 422 = 21 m
Width of the road = 3.5 m …[Given]
Radius of the outer circle (R)
= radius (r) + width of the road
= 21 + 3.5
= 24.5 m
Area of the road = area of outer circle – area of circular garden
= πR² – πr²
= π (R² – r²)
= 227 [(24.5)² – (21)²]
= 227 (24.5 + 21) (24.5 – 21)
…..[∵ a²-b² = (a+b)(a-b)]
= 227 x 45.5 x 3.5
= 22 x 45.5 x 0.5
= 500.50 sq. m
∴ The area of the road is 500.50 sq. m.

Question 4.
Find the area of the circle if its circumference is 88 cm.
Solution:
Circumference of the circle = 88 cm …[Given]
Circumference of the circle = 2πr
∴ 88 = 2 x 227 x r
∴ r=88×72×22 ∴ r = 14cm
Area of the circle = πr² = 227 x (14)²
= 227 x 14 x 14 = 22 x 2 x 14 = 616 sq. cm
∴ The area of circle is 616 Sq cm

Intext Questions and Activities

Question 1.
Draw a circle of radius 28mm. Draw any one triangle and draw a trapezium on the graph paper. Find the area of these figures by counting the number of small squares on the graph paper. Verify your answers using formula for area of these figures.
Observe that smaller the squares of graph paper, better is the approximation of area. (Textbook pg. no. 105)
Solution:
(Students should do this activity on their own.)

Download PDF

Maharashtra Board Solutions Class 8-Maths (Practice Set 15.6): Chapter 15- Area

Download PDF: Maharashtra Board Solutions Class 8-Maths (Practice Set 15.6): Chapter 15- Area PDF

Chapterwise Maharashtra Board Solutions Class 8 Maths :

• Chapter 1- Rational and Irrational Numbers (Practice Set 1.1)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.2)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.3)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.4)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.1)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.2)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.3)
• Chapter 3- Indices and Cube Root (Practice Set 3.1)
• Chapter 3- Indices and Cube Root (Practice Set 3.2)
• Chapter 3- Indices and Cube Root (Practice Set 3.3)
• Chapter 4- Altitudes and Medians of a Triangle (Practice Set 4.1)
• Chapter 5- Expansion Formulae (Practice Set 5.1)
• Chapter 5- Expansion Formulae (Practice Set 5.2)
• Chapter 5- Expansion Formulae (Practice Set 5.3)
• Chapter 5- Expansion Formulae (Practice Set 5.4)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.1)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.2)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.3)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.4)
• Chapter 7- Variation (Practice Set 7.1)
• Chapter 7- Variation (Practice Set 7.2)
• Chapter 7- Variation (Practice Set 7.3)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.1)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.2)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.3)
• Chapter 9- Discount and Commission (Practice Set 9.1)
• Chapter 9- Discount and Commission (Practice Set 9.2)
• Chapter 10- Division of Polynomials (Practice Set 10.1)
• Chapter 10- Discount and Commission (Practice Set 10.2)
• Chapter 11- Statistics (Practice Set 11.1)
• Chapter 11- Statistics (Practice Set 11.2)
• Chapter 11- Statistics (Practice Set 11.3)
• Chapter 12- Equations in One Variable (Practice Set 12.1)
• Chapter 12- Equations in One Variable (Practice Set 12.2)
• Chapter 13- Congruence of Triangles (Practice Set 13.1)
• Chapter 13- Congruence of Triangles (Practice Set 13.2)
• Chapter 14- Compound Interest (Practice Set 14.1)
• Chapter 14- Compound Interest (Practice Set 14.2)
• Chapter 15- Area (Practice Set 15.1)
• Chapter 15- Area (Practice Set 15.2)
• Chapter 15- Area (Practice Set 15.3)
• Chapter 15- Area (Practice Set 15.4)
• Chapter 15- Area (Practice Set 15.5)
• Chapter 15- Area (Practice Set 15.6)
• Chapter 16- Surface Area and Volume (Practice Set 16.1)
• Chapter 16- Surface Area and Volume (Practice Set 16.2)
• Chapter 16- Surface Area and Volume (Practice Set 16.3)
• Chapter 17- Factorisation of Algebraic Expressions (Practice Set 17.1)
• Chapter 17- Factorisation of Algebraic Expressions (Practice Set 17.2)