Chapter 11 · Areas Related to Circles

NCERT Exemplar Class 10 Maths Exercise 11.1

All 10 questions of NCERT Exemplar Class 10 Maths Exercise 11.1 (Areas Related to Circles), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   If ​the sum of the areas of ​two circles ​with radii $R_1$ and $R_2$ is ​equal ​to the ​area of a circle of radius $R$, then

   1. (a)$R_1+R_2=R$
   2. (b)$R_1^2+R_2^2=R^2$
   3. (c)$R_1+R_2<R$
   4. (d)$R_1^2+R_2^2<R^2$
   Show answer

   (b) $R_1^2+R_2^2=R^2$

   Step-by-step solution →
2. Q2
   If the sum of the ​circumferences of two circles ​with radii $R_1$ ​and $R_2$ is equal to the circumference of ​a ​circle of ​radius $R$, then

   1. (a)$R_1+R_2=R$
   2. (b)$R_1+R_2>R$
   3. (c)$R_1+R_2<R$
   4. (d)Nothing definite can be said about the relation among $R_1$, $R_2$ and $R$.
   Show answer

   (a) $R_1+R_2=R$

   Step-by-step solution →
3. Q3
   If ​the circumference ​of ​a ​circle ​and the perimeter of a square are ​equal, then

   1. (a)Area of the circle = Area of the square
   2. (b)Area of the circle > Area of the square
   3. (c)Area of the circle < Area of the square
   4. (d)Nothing definite can be said about the relation between the areas of the circle and square.
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   (b) Area of the circle > Area of the square

   Step-by-step solution →
4. Q4
   Area ​of ​the largest ​triangle ​that can be ​inscribed in a semi-circle of radius $r$ ​units is

   1. (a)$r^2$ sq. units
   2. (b)$\frac{1}{2}{r}^2$ sq. units
   3. (c)$2r^2$ sq. units
   4. (d)$\sqrt{2}{r}^2$ sq. units
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   (a) $r^2$ sq. units

   Step-by-step solution →
5. Q5
   If the perimeter of ​a circle is ​equal ​to that of a square, then ​the ​ratio of ​their ​areas is

   1. (a)$22:7$
   2. (b)$14:11$
   3. (c)$7:22$
   4. (d)$11:14$
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   (b) $14:11$

   Step-by-step solution →
6. Q6
   It is proposed to ​build a single circular ​park equal in area to the sum of ​areas of ​two circular parks of diameters 16 ​m and 12 m in a ​locality. ​The radius of the new park would be

   1. (a)10 m
   2. (b)15 m
   3. (c)20 m
   4. (d)24 m
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   (a) 10 m

   Step-by-step solution →
7. Q7
   The ​area of the ​circle ​that ​can ​be inscribed ​in a square ​of ​side 6 cm is

   1. (a)$36\pi$ cm${}^2$
   2. (b)$18\pi$ cm${}^2$
   3. (c)$12\pi$ cm${}^2$
   4. (d)$9\pi$ cm${}^2$
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   (d) $9\pi$ cm${}^2$

   Step-by-step solution →
8. Q8
   The ​area ​of the ​square ​that can be inscribed ​in a circle ​of ​radius $8$ cm is

   1. (a)$256{\text{cm}}^2$
   2. (b)$128{\text{cm}}^2$
   3. (c)$64\sqrt{2}{\text{cm}}^2$
   4. (d)$64{\text{cm}}^2$
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   (b) $128{\text{cm}}^2$

   Step-by-step solution →
9. Q9
   The ​radius of a circle whose circumference is equal to the ​sum ​of the circumferences of the two ​circles ​of ​diameters $36\text{cm}$ and $20\text{cm}$ is

   1. (a)56 cm
   2. (b)42 cm
   3. (c)28 cm
   4. (d)16 cm
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   (c) 28 cm

   Step-by-step solution →
10. Q10
    The diameter of a circle ​whose area is ​equal to ​the sum of the areas of the two circles ​of ​radii 24 cm and 7 cm ​is

    1. (a)31 cm
    2. (b)25 cm
    3. (c)62 cm
    4. (d)50 cm
    Show answer

    (d) 50 cm

    Step-by-step solution →