Exercise 11.1 Archives - Noon Academy

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A)
$22:7$
(B)
$14:11$
(C)
$7:22$
(D)
$11:14$

The correct option is (B) \[14:11\] Explanation: Let us take r as the radius of the circle and a as the side of the square. From the given question, Perimeter of a circle of radius r = Perimeter of...

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (A)
${{r}^{2}}$
sq. units (B)
$\frac{1}{2}{{r}^{2}}$
sq. units (C)
$2{{r}^{2}}$
sq. units (D)
$\sqrt{2}{{r}^{2}}$
sq. units

The correct option is (A) \[{{r}^{2}}\] sq. units Explanation: The largest triangle which can be inscribed in a semi-circle of radius r units is Base of triangle should be equal to the diameter of...

If the circumference of a circle and the perimeter of a square are equal, then (A) Area of the circle = Area of the square (B) Area of the circle > Area of the square (C) Area of the circle < Area of the square (D) Nothing definite can be said about the relation between the areas of the circle & square.

The correction option is (B) Area of the circle > Area of the square Explanation: From the given question, Circumference of a circle of radius r = Perimeter of a square of side a Let us take r...

If the sum of the circumferences of two circles with radii
$R1$
and
$R2$
is equal to the circumference of a circle of radius
$R$
, then (A)
${{R}_{1}}+{{R}_{2}}=R$
(B)
${{R}_{1}}+{{R}_{2}}>R$
(C)
${{R}_{1}}+{{R}_{2}}<R$
(D) Nothing definite can be said about the relation among
${{R}_{1}}$
,
${{R}_{2}}$
&
$R$
.

The Correct option(A) \[{{R}_{1}}+{{R}_{2}}=R\] Explanation: From the given question, We got sum of the circumferences of two circles with radii \[R1\] and \[R2\] is equal to the circumference of a...

If the sum of the areas of two circles with radii
$R1$
and
$R2$
is equal to the area of a circle of radius
$R$
, then (A)
${{R}_{1}}+{{R}_{2}}=R$
(B)
$R_{1}^{2}+R_{2}^{2}={{R}^{2}}$
(C)
${{R}_{1}}+{{R}_{2}}<R$
(D)
$R_{1}^{2}+R_{2}^{2}<{{R}^{2}}$

The Correct option is (B) \[R_{1}^{2}+R_{2}^{2}={{R}^{2}}\] Explanation: From the given question, We got sum of the areas of two circles with radii \[R1\] and \[R2\] is equal to the area of a circle...

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If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) (B) (C) (D)

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (A) sq. units (B) sq. units (C) sq. units (D) sq. units

If the sum of the circumferences of two circles with radii and is equal to the circumference of a circle of radius , then (A) (B) (C) (D) Nothing definite can be said about the relation among , & .

If the sum of the areas of two circles with radii and is equal to the area of a circle of radius , then (A) (B) (C) (D)

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A)
$22:7$
(B)
$14:11$
(C)
$7:22$
(D)
$11:14$

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (A)
${{r}^{2}}$
sq. units (B)
$\frac{1}{2}{{r}^{2}}$
sq. units (C)
$2{{r}^{2}}$
sq. units (D)
$\sqrt{2}{{r}^{2}}$
sq. units

If the sum of the areas of two circles with radii
$R1$
and
$R2$
is equal to the area of a circle of radius
$R$
, then (A)
${{R}_{1}}+{{R}_{2}}=R$
(B)
$R_{1}^{2}+R_{2}^{2}={{R}^{2}}$
(C)
${{R}_{1}}+{{R}_{2}}<R$
(D)
$R_{1}^{2}+R_{2}^{2}<{{R}^{2}}$