Question

4. The ratio of circumference to the diameter of the circle if its
original radius is tripled is
5. A man bought a rectangular field of length 144m and width 64m.
In exchange for this field he wanted to buy a square field of the
same area. The side of the square field would be how many m.​

Answer 1

AnswEr :

Question 4.

The ratio of circumference to the diameter of the circle if its original radius is tripled is?

Solution :

Let the Original Radius be r. But after tripled.

◗ New Radius = 3 × r = 3r

◗ Diameter = 2 × Radius = (2 × 3r) = 6r

• Let's Head to the Question Now :

⇒ Circumference : Diameter

⇒ 2πr : Diameter

⇒ 2π × 3r : 6r

⇒ 6πr : 6r

• Dividing both term by 6r

⇒ π : 1

⇒ $\dfrac{22}{7}$ : 1

⇒ 22 : 7

⠀

∴ Ratio will be 22 : 7, if it will tripled.

$\rule{300}{2}$

Question 5.

A man bought a rectangular field of length 144m and width 64m.In exchange for this field he wanted to buy a square field of the same area. The side of the square field would be how many m.

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{64 m}}}\put(7.7,1){\large{B}}\put(9.2,0.7){\matsf{\large{144 m}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

• AREA OF THE RECTANGULAR FIELD :

⇒ Area = Length × Breadth

⇒ Area = 144m × 64m

He want to buy a square field of Same Area, then that will be Area of Square Field.

$\rule{300}{1}$

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{Side}}}\put(7.7,1){\large{B}}\put(9,0.7){\matsf{\large{Side}}}\put(10.6,1){\large{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){2}}\put(10.5,1){\line(0,3){2}}\put(8,3){\line(3,0){2.5}}\put(10.6,3){\large{D}}\end{picture}$

• According to the Question Now :

↠ Area of Square = Area of Rectangle

↠ ( Side )² = (144m × 64m)

↠ Side = √(144 × 64)m²

↠ Side = √(12 × 12 × 8 × 8)m²

↠ Side = (12 × 8)m

↠ Side = 96 m

⠀

∴ Side of Square Field will be 96 m.

#answerwithquality #BAL

Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\green{ANSWER\:4\::}}}}}}$

$\bf{\Large{\underline{\bf{\orange{Given\::}}}}}$

The circle of its original radius is tripled.

$\bf{\Large{\underline{\bf{\red{To\:find\::}}}}}$

The ratio of circumference to the diameter of circle.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

We know that circumference of circle: 2πr

We know that diameter of circle: 2r

A/q

Let the original radius[r] of circle be 3R

∴ Diameter of circle = 2r = 2(3R) = 6R

Now,

→ Circumference of circle : diameter of circle

→ 2πr : 2r

→ 2π3R : 6R

→ 6Rπ : 6R

→ $\bf{\cancel{6R}\pi \::\:\cancel{6R}}$

→ π : 1

→ $\bf{\frac{22}{7} \::\:1}$          [π = 22/7]

→ 22 : 7

$\bf{\Huge{\underline{\boxed{\bf{\green{ANSWER\:5\::}}}}}}$

$\bf{\Large{\underline{\bf{\orange{Given\::}}}}}$

A man bought a rectangular field of length 144m and width 64m. In exchange for this field he wanted to buy a square field of the same area.

$\bf{\Large{\underline{\bf{\red{To\:find\::}}}}}$

The side of the square field in metres.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

$\bf{We\:have}\begin{cases} \sf{The\:length\:of\:rectangular\:field=144m}\\ \sf{The\:breadth\:of\:rectangular\:field=64m}\end{cases}}$

We know that area of rectangle: (Length × Breadth)   [sq.units]

→ Area of rectangular field = (144 × 64)m²

→ Area of rectangular field = (9261)m²

We know that area of square: (side×side)   [sq.units]

Area of square equal to area of rectangular field according to the question;

→ Let the square field side be M

→ (M)² = 9261m²

→ M = √9261m²

→ M = 96 m

Thus,

The side of the square field is 96m.