Tag: circle measures

Questions Related to circle measures

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.