KSEEB Solutions for Class 10 Maths Chapter 5 Areas Related to Circles Additional Questions

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Karnataka State Syllabus Class 10 Maths Chapter 5 Areas Related to Circles Additional Questions

I. Multiple Choice Questions:

Question 1.
The radius of a circle is 5cm, then its area is
a) 154 cm³
b) 1386 cm³
c) 169 cm³
d) 308 cm³
Answer:
a) 154 cm³

Question 2.
The diameter of a semicircle is 4cm Its area is.
a) π cm²
b) 2π cm²
c) 4π cm²
d) 8π cm²
Answer:
b) 2π cm²

Question 3.
The radii of two concentric circles are 3cm and 2cm. the ratio of their areas.
a) 3 : 4
b) 9 : 2
c) 9 : 4
d) 4 : 3
Answer:
c) 9 : 4

Question 4.
The diameter of a circle whose area is equal to the areas of two circles of radii 24cm and 7cm is
a) 25 cm
b) 31 cm
c) 28 cm
d) 50 cm
Answer:
d) 50 cm

Question 5.
The radius of a circle is 21cm then its circumference is
a) 66 cm
b) 33 cm
c) 132 cm
d) 99 cm
Answer:
c) 132 cm

Question 6.
Formula to find area of Quadrant is
a) \(\frac{\pi r^{2}}{2}\)
b) πr²
c) \(\frac{\pi r^{2}}{3}\)
d) \(\frac{\pi r^{2}}{4}\)
Answer:
d) \(\frac{\pi r^{2}}{4}\)

Question 7.
Find the perimeter of a Quadrant of a circle of radius 7cm.
a) 25 cm
b) 49 cm
c) 14 cm
d) 66 cm.
Answer:
a) 25 cm

Question 8.
If the perimeter and the area of a circle are equal numerically, then the diameter of the circle is.
a) 8 units.
b) n units
c) 4 units
d) 2 units.
Answer:
c) 4 units

Question 9.
The central angle of a Quadrant of a circle measures.
a) 60°
b) 90°
c) 120
d) 30°
Answer:
b) 90°

Question 10.
The measure of the central angle of a circle is.
a) 360°
b) 180°
c) 270°
d) 90°
Answer:
a) 360°

Question 11.
If the diameter of a semi-circular protractor is 7cm, then its perimeter is
a) 7 cm
b) 36 cm
c) 21 cm
d) 18 cm
Answer:
d) 18 cm

Question 12.
The external and internal radius of a circular path are 5m and 3m respectively. The area of the circular path is.
a) 87π m²
b) 167π m²
c) 157π m²
d) 327π m²
Answer:
b) 167π m²

Question 13.
Find the area of a ring-shaped region enclosed between two concentric circles of diameter 8cm and 6cm.
a) 22 cm²
b) 44 cm²
c) 66 cm²
d) 88 cm²
Answer:
a) 22 cm²

Question 14.
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is.
a) 11 : 4
b) 22 : 7
c) 14 : 1
d) 7 : 22
Answer:
c) 14 : 1

Question 15.
The area of circle whose circumference is 44cm is
a) 77 cm²
b) 308 cm²
c) 168 cm²
d) 154 cm²
Answer:
d) 154 cm²

Question 16.
A bicycle wheel makes 2500 revolutions in moving. 11km. Find the circumference of the wheel.
a) 220 cm
b) 55 cm
c) 110 cm
b) 100 cm.
Answer:
c) 110 cm

Question 17.
The minute hand of a clock is of length 4cm. then the angle swept by the minute hand in 15 minutes.
a) 45°
b) 60°
c) 120
d) 90°
Answer:
d) 90°

Question 18.
The perimeter of the sector with radius 10.5cm and sector angle 60° is
a) 23 cm
b) 32 cm
c) 35 cm
d) 28 cm
Answer:
b) 32 cm

Question 19.
The radius of a semicircular protractor is 35m. then its perimeter.
a) 90 m
b) 45 m
c) 180 m
d) I20 m.
Answer:
c) 180 m

Question 20.
The area swept out by a horse tied in a rectangular grass field with a rope 8m long is
a) 647π m²
b) 327π m²
c) 128π m²
a) 48π m²
Answer:
a) 647π m²

Question 21.
The area (in cm²) of the circle that can be inscribed in a square of side 8cm is.
a) 64π
b) 16π
c) 8π
d) 32π
Answer:
b) 16π

Question 22.
The area of a circle that can be inscribed in a square, of side 10cm is
a) 407π cm²
b) 307π cm²
c) 1007π cm²
d) 257π cm²
Answer:
d) 257π cm²

Question 23.
The area of the largest triangle that can be inscribed in a semicircle of radius r is
a) r²
b) 2r²
c) r²
d) 2r³
Answer:
a) r²

Question 24.
The area of the largest square that can be inscribed in a circle of radius 12cm is.
a) 24 cm²
b) 249 cm²
c) 288 cm²
d) 196 \(\sqrt{2}\) cm²
Answer:
c) 288 cm²

Question 25.
The perimeter of a square circumscribing a circle of radius a unit is
a) 2a units
b) 4a units
c) 8a units
d) 16a units.
Answer:
c) 8 a units

II. Short Answer Questions:

Question 1.
Find the area of the circle inscribed in a square of side b cm.

Answer:
Diameter of a circle = b ; r = b/2

Question 2.
Find the area of a square inscribed in a circle of radius a.

Answer:
radius = a & diameter = 2a
Diagonal of square = 2a
AC² = AB² + BC²
(2a)² = (side)² + (side)²
4a² = 2side²

Area of square = side2 = 2a2.

Question 3.
If the diameter of semicircular protractor is 14 cm then find its perimeter.
Answer:
Perimeter of semicircular protractor
= πr + diameter
= \(\frac{22}{7}\) × 7 + 14 = 22 + 14 = 36 cm.

Question 4.
Find the number of revolutions if circumference of a wheel is 22cm and travells a distance 110km.
Answer:
Number of revolutions

Question 5.
If circumference and the area of a circle are numerically equal, find the diameter of the circle
Answer:
2πr = πr²
2r = r²
r = 2
d = 2r = 2 × 2 = 4 units.

Question 6.
Difference between the circumference and radius of a circle is 37cm. Find the area of circle.
Answer:
2πr – r = 37
r(2π – 1) = 37
pppppppp

Question 7.
Find the radius the area of a circular playground is 22176m²
Answer:
Area of circular playground = 22176 m²
πr2 = 22176
\(\frac{22}{7}\) r² = 22176
r = 84 m

III. Long Answer Questions.

Question 1.
The area of a circular playground is 2217m². Find the cost of fencing this ground at the rate of? 50 per/m.
Answer:
Area of circular playground

= 44 x 12
= 528 m
Cost of fencing this ground
= 528 x 50
= ₹ 26400

Question 2.
The circumference of a circle exceeds the diameter by 16.8cm. Find the radius of the circle.
Answer:
Let the radius of circle be r cm.
∴ Diameter = 2r cm
circumference = 2πr cm
circumference = 16.8 + Diameter
2πr = 16.8 + 2r

Hence radius is 3.92 cm

Question 3.
A race track is in the form of a ring whose inner circumference is 352m, and the outer circumference is 396 in. Find the width of the track.
Answer:
Inner circumference = 352m
27πr = 352m

∴ Width of track = R – r = 63 – 56 = 9m

Question 4.
The minute hand of a clock is 10cm long. Find the area of the face of the clock described by the minute hand between 10 AM and 10-30 AM.
Answer:
Angle described by the minute hand in one minute = 6°
∴ Angle describes by minute hand between 10 AM and 10.30 Am = 30 minutes = 30 x 6 = 180°
∴ Area swept by the minute hand in 30 minutes
= Area of sector of circle radius 10cm

Question 5.
A circle of radius 6cm is inscribed in a square as shown in the given figure. Find the shaded region.

Answer:
From the figure, side of a square = Diameter of a circle = 2r
= 2 x 6 = 12cm
∴ Area of square = (side)²
= (12)² = 144cm²

∴ Area of the shaded region
= Area of square-Area of the circle
= 144 – 133.04
= 30.96 cm²

Question 6.
Find the length of the arc that subtends an angle of 72° at the centre of a circle of radius 5cm.
Answer:

Question 7.
In the given figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10cm as centers, to intersect the sides BC, CA and AB at their respective midpoints D,E and F. Find the area of the shaded region.

Answer:
= \(\frac{1}{2}\) (Side of equilateral ∆^le)
= \(\frac{1}{2}\) × 10 = 5 cm
Area of shaded region
= Sum of areas of there equal sectors

Question 8.
A paper is in the form of a rectangle ABCD in which AB = 18 cm and BC = 14cm. A semicircle with BC as diameter is cut off. Find the area of the remaining portion.

Answer:
∴ Area of rectangle ABCD = l × b
= AB × BC
= 18 × 14 = 252 cm²
Radius of semicircle (r)

Area of the remaining portion
= 252 – 77
= 175cm²