Tag: the area of ring

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Questions Related to the area of ring

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

Jackson measured the button on his shirt. Then he calculated that it has a semicircle of $25.12\ mm$. What is the button's radius? (Use $\pi = 3.14$).

  1. $1\ mm$
  2. $2\ mm$
  3. $3\ mm$
  4. $4\ mm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of a semicircle $=\dfrac{1}{2}\pi r^2$
$ 25.12= \dfrac{1}{2}\pi r^2$
$ 50.24= \pi r^2  $

Using $\pi = 3.14$ (given)
$16 = r^2$
$r = 4\ mm$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

A circular grassy plot of land, 42 m in diameter, has a path 3.5 m wide running around it on the outside. Find the cost graveling the path at Rs 4 per square meter.

  1. $Rs 2002$
  2. $Rs 2003$
  3. $Rs 2004$
  4. $Rs 2000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given : Radius ($r _1$) $=21m$

             Radius ($r _2$) $=24.5m$

Required area $=\pi (r _2^{2}-r _1^{2})$

Required area $=\pi (24.5^{2}-21^{2})=500.5$

Cost $=500.5\times 4$

         $=2002Rs$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The front wheels of a wagon are $2$ m in circumference and the back wheels are $3$ m feet in circumference. When the front wheels have made $10$ more revolutions than the back wheels, how many metres has the wagon travelled?

  1. $40$ feet
  2. $50$ feet
  3. $60$ feet
  4. $80$ feet
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the back wheels make n revolutions. Then front wheels make n+10 revolutions. Distance travelled by front = 2(n+10) and by back = 3n. Equating: 2(n+10) = 3n, so 2n+20 = 3n, giving n=20. Distance = 3*20 = 60 feet.

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The area in ( ${cm^2}$) of the largest triangle that can be inscribed in a semicircle of radius r cm is 

  1. ${\cfrac{1}{3}\pi r^2}$
  2. ${2r^2}$
  3. ${r^2}$
  4. ${\cfrac{1}{2}\pi r^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The largest triangle inscribed in a semicircle has a height = radius of the circle

base = diameter of the circle
$\therefore$ Area of a triangle $=\dfrac{1}{2}\times base\times height$
                                  $=\dfrac{1}{2}\times 2r \times r=r^2$
Hence, option C is correct.

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

Radius of a marry-go-round is $7\ m$. At its edge, at equal distances swings are suspended. If length of an arc between two successive swings is $4$ metre, then find the number of swings that marry-go-round has.

  1. $13\ swings$.
  2. $11\ swings$.
  3. $15\ swings$.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius of the merry go round, r = 7m

Perimeter of the merry go round = 2 x pi x r = 2 x 22 / 7 x 7 = 44 m
Arc distance between two swings = 4 m
Hence nos. of swings, n on a circle, should satisfy the following equation:
nx arc distance between two swings = Perimeter of the merry go round
Hence, n x 4 = 44
Hence, n = 44/4 = 11
Hence there are 11 swings on the merry go round.
Correct answer is option (B)

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is

  1. $r^2$ sq. units
  2. $\dfrac{1}{2} r^2$ sq. units
  3. $2r^2$ sq. units
  4. $\sqrt{2} r^2$ sq. units
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a triangle is equal to the base times the height.
In a semi circle, the diameter is the base of the semi-circle.
This is equal to $2\times r$ (r = the radius)
If the triangle is an isosceles triangle with an angle of $45^\circ$ at each end, then the height of the triangle is also a radius of the circle.
A = $\frac{1}{2} \times b \times h$ formula for the area of a triangle becomes
A = $\frac{1}{2}\times 2 \times r \times r$ because:
The base of the triangle is equal to $2\times r$
The height of the triangle is equal to r
A = $\frac{1}{2} \times 2 \times r \times r$ becomes:
A = $r^2$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If a circular grass lawn of $35\ m$ in radius has a path $7\ m$ wide running around it on the outside, then the area of the path is

  1. $1450\ m^2$
  2. $1576\ m^2$
  3. $1694\ m^2$
  4. $3368\ m^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius of bigger circle(with the path) = $35 + 7 = 42\ m.$
Thus area of the path $=$ Area of bigger circle $-$ Area of smaller circle
$\therefore$ Required area $= \pi (42)^2 - \pi (35)^2 = \dfrac{22}{7} \times (42 + 35)(42 - 35) = 22 \times 77 = 1694\ m^2$