Tag: circle measures

Questions Related to circle measures

The semicircle temperature dial on a thermostat has a radius of $2\ cm$. What is the dial's area?

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

  1. $6.20\ cm^2$

  2. $3.28\ cm^2$

  3. $4.28\ cm^2$

  4. $6.28\ cm^2$

Show answer
Correct Option: D
Explanation:

Area of a semicircle $=\dfrac{1}{2}\pi r^2$
$ = \dfrac{1}{2}\pi (2)^2$
$ = 2\pi  $

$ = 2 \times 3.14$
$= 6.28$ $cm^2$

A lounge has a semicircular rug with a diameter of $4\ m$. What is the area of the rug?

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

  1. $6.20$ $m^2$

  2. $3.28$ $m^2$

  3. $4.28$ $m^2$

  4. $6.28$ $m^2$

Show answer
Correct Option: D
Explanation:

radius $= 2\ m$
Area of a semicircle $= \dfrac{1}{2}\pi r^2$
$ = \dfrac{1}{2}\pi (2)^2$
$ = 2\pi  $

$ = 2 \times 3.14$
$= 6.28$ $m^2$

Evaluate the area of the semicircle if its circumference is $15.15\ cm$? (Use $\pi = 3$)

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

  1. $7.475$ $cm^2$

  2. $6.575$ $cm^2$

  3. $4.575$ $cm^2$

  4. $7.575$ $cm^2$

Show answer
Correct Option: D
Explanation:

Circumference of a semicircle $=\pi r$
$15.15= \pi r$
$r = 5.05$
Area of the semicircle $=\dfrac{1}{2}\pi r$
$=\dfrac{1}{2}\pi \times 5.05$
$= 7.575$ $cm^2$

What is the area of the semicircle if its circumference is $12.5\ cm$?

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

  1. $6.28$ $cm^2$

  2. $4.28$ $cm^2$

  3. $2.28$ $cm^2$

  4. $1.28$ $cm^2$

Show answer
Correct Option: A
Explanation:

Circumference of a semicircle $=\pi r$
$12.5= \pi r$
$r = 3.98 \approx 4$
Area of the semicircle $=\dfrac{1}{2}\pi r$
$=\dfrac{1}{2}\pi (4)$
$= 6.28$ $cm^2$

Calculate the area of a circular ring whose outer and inner radii are $12$ and $10\ cm.$

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

  1. $118.16$ $cm^2$

  2. $128.16$ $cm^2$

  3. $138.16$ $cm^2$

  4. $148.16$ $cm^2$

Show answer
Correct Option: C
Explanation:

Area of a circular ring $=\pi(R^2-r^2)$
$=3.14(12^2-10^2)$
$= 3.14 \times 44$
$= 138.16$ $cm^2$

The area of the semicircle is $200\ m^2$. What is the radius of the semicircle?

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

  1. $10\ m$

  2. $11\ m$

  3. $12\ m$

  4. $13\ m$

Show answer
Correct Option: B
Explanation:

Area of a semicircle $=\dfrac{1}{2}\pi r^2$
$200 = \dfrac{1}{2}\pi r^2$
$400 = \pi r^2 $
$r^2=127.38\ m^2$
$r \approx 11$ $m$

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 $\pi = 3.14$).

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

  1. $1\ mm$

  2. $2\ mm$

  3. $3\ mm$

  4. $4\ mm$

Show answer
Correct Option: D
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)
$16 = r^2$
$r = 4\ mm$

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.

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

  1. $Rs 2002$

  2. $Rs 2003$

  3. $Rs 2004$

  4. $Rs 2000$

Show answer
Correct Option: A
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 $=500.5\times 4$

         $=2002Rs$

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?

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

  1. $40$ feet

  2. $50$ feet 

  3. $60$ feet

  4. $80$ feet

Show answer
Correct Option: C

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

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

  1. ${\cfrac{1}{3}\pi r^2}$

  2. ${2r^2}$

  3. ${r^2}$

  4. ${\cfrac{1}{2}\pi r^2}$

Show answer
Correct Option: C
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.