[3 marks sum] - Mathematics STD 10 Questions - Vidyadip

Questions

[3 marks sum]

🎯

Test yourself on this topic

15 questions · timed · auto-graded

Question 13 Marks

A cart wheel makes $9$ revolutions per second. If the diameter of the wheel is $42\ cm,$ find its speed in km/hr.

Answer

$\text { Circumference }=2 \pi r =\pi d $
$=\frac{22}{7} \times 42 $
$=132 cm =1.32 m $
$\text { Circumference }=1.32 m$
No. of revolutions $=9$ per second
No. of revolutions per hour $=9 \times 60 \times 60=32400$
Distance covered in one hour $=32400 \times 1.32=42768\ m / hour$
Speed of the wheel in km/hour $=\frac{42768}{1000}=42.768\ km / hour =43\ km / hr$
Speed $=43\ km / hr$

View full question & answer→

Question 23 Marks

The speed of the car is $66$ km/hour. If each wheel of the car is $140\ cm$ in diameter, find the number of revolutions made by each wheel per minute.

Answer

$\text { Circumference }=2 \pi r =\pi d $
$=\frac{22}{7} \times 140 $
$=440 cm =4.4 m $
$\text { Circumference }=4.4 m $
$\text { Distance travelled in one hour }=66 k m =66000 m $
$\text { Distance travelled in one minute }=\frac{66000}{60}=1100 m $
$\text { No. of revolutions in one minute }=\frac{\text { Distance }}{\text { Circumference }} $
$=\frac{1100}{4.4} $
$=250$
No. of revolutions made by each wheel $=250\ rpm$.

View full question & answer→

Question 33 Marks

The wheel of the car makes 10 revolutions per second. If its diameter is 70 cm, find the speed of the car in km per hour.

Answer

Circumference $=2 \pi r=\pi d$
$
=\frac{22}{7} \times 70=220 cm =2.2 m
$
Circumference $=2.2 m$
No. of revolutions $=10$ per second
No. of revolutions per hour $=10 \times 60 \times 60=36000$
Distance covered in one hour $=36000 \times 2.2=79200 m /$ hour
Speed of the car in km/hour $=\frac{79200}{1000}=79.2 km /$ hour
Speed $=79.2 km / hr$

View full question & answer→

Question 43 Marks

The diameter of a wheel is 1.4m. How many revolutions does it make in moving a distance of 2.2 kms?

Answer

Diameter of the wheel $=1.4 m$
Circumference $=2 \pi r=\pi d$
$=\frac{22}{7} \times 1.4$
$=4.4 m$
Circumference $=8.8 m$
Distance travelled $=2.2 km =2200 m$
No. of revolutions $=\frac{2200}{4.4}=500$
Wheel makes 500 revolutions in travelling $2.2 km$

View full question & answer→

Question 53 Marks

Find the circumference of the circle whose area is $81 \pi cm ^2$.

Answer

Area = $\pi r^2\pi r^2 = 81 \pi$
$r^2 = 81$
$r = 9 cm$
circumference = $2 \pi r$
$= 2 \times \pi \times 9$
$= 18 \pi cm$
araJmference - $18 \pi cm$

View full question & answer→

Question 63 Marks

Find the area of a circular field that has a circumference of $396$ m.

Answer

$\text { Circumference }=396 m $
$2 \pi r=396 $
$2 \times \frac{22}{7} \times r=396 m $
$r=396 m \times \frac{7}{22} \times \frac{1}{2} $
$r=63 m $
$\text { Area }=\pi r^2 $
$=\frac{22}{7} \times 63 \times 63 $
$=12474 m ^2$
Area of the circular field $=12474 m ^2$

View full question & answer→

Question 73 Marks

A horse is tied with a 21 m laig rope to the corner of a field which is in the shape of an equilateral triangle. Find the area of the field over which it can graze.

Answer

An equilateral triangle has all angles of 60 degrees
The horse will be able to graze over a sector of a circle of radius $21 cm$ and angle 60 , so
$\text { Area }=\frac{60^{\circ}}{360^{\circ}} \pi r ^2$
$=\frac{60^{\circ}}{360^{\circ}} \times \frac{22}{7} \times 21 \times 21$
$=231 m ^2$
Horse can graze in $231 m ^2$

View full question & answer→

Question 83 Marks

Find the area and perimeter of the following sector :Diameter $= 42\ cm,$ angle at the centre is $100·.$

Answer

Diameter $=2 r$
$\Rightarrow r =\frac{\text { diameter }}{2}=\frac{42}{2}=21 cm$
Area of the sector $=\left(\pi r ^2 \times \frac{\theta}{360^{\circ}}\right)$
$=\frac{22}{7} \times 21 \times 21 \times \frac{100^{\circ}}{360^{\circ}} $
$=385 cm ^2$
$\text { Peri meter of the sector }=2 r +\left(2 \pi r \times \frac{\theta}{360^{\circ}}\right) $
$=2 \times 21+\left(2 \times \frac{22}{7} \times 21 \times \frac{100^{\circ}}{360^{\circ}}\right) $
$=42+36.66 $
$=78.66\ cm$
Area of the sector $=385 cm ^2$ and perimeter $=78.66 cm$

View full question & answer→

Question 93 Marks

Find the area and perimeter of the following sector :Radius $= 6\ cm,$ angle at the centre is $70^\circ$

Answer

Area of the sector $=\pi r ^2 \times \frac{\theta}{360^{\circ}}$
$=\frac{22}{7} \times 6 \times 6 \times \frac{70^{\circ}}{360^{\circ}}$
$=22 cm ^2$
$\text { Perimeter of the sector }=2 r +\left(2 \pi r \times \frac{\theta}{360^{\circ}}\right) $
$=2 \times 6+\left(2 \times \frac{22}{7} \times 6 \times \frac{70^{\circ}}{360^{\circ}}\right) $
$=12+7.33 $
$=19.33\ cm$
Area of the sector $=22\ cm ^2$ and perimeter $=19.33\ cm$

View full question & answer→

Question 103 Marks

Find the area and perimeter of the following sector :Radius= 4.2 cm, angle at the centre is 60 °

Answer

$\text { Area of the sector }=\left(\pi r ^2 \times \frac{\theta}{360^{\circ}}\right)$
$=\frac{22}{7} \times 4.2 \times 4.2 \times \frac{60^{\circ}}{360^{\circ}}$
$=9.24 cm ^2$
Peri meter of the sector
$=2 r +\left(2 \pi r \times \frac{\theta}{360^{\circ}}\right)$
$=2 \times 4.2+\left(2 \times \frac{22}{7} \times 4.2 \times \frac{60^{\circ}}{360^{\circ}}\right)$
$=8.4+4.4$
$=12.8 cm$
Area of the sector $=9.24 cm ^2$ and perimeter $=12.8 cm$

View full question & answer→

Question 113 Marks

Find the area and perimeter of the following semi-circle :Diameter $= 5.6\ cm$

Answer

$\text { Diameter }=2 r $
$\Rightarrow r =\frac{\text { diameter }}{2}=\frac{5.6}{2}=2.8 cm $
$\text { Area of the semi-circle }=\frac{1}{2} \pi r ^2 $
$=\frac{1}{2} \times \frac{22}{7} \times 2.8 \times 2.8 $
$=12.32\ cm ^2$
Peri meter of the semi-cir de $=(\pi r+2 r)$
$=\left(\frac{22}{7} \times 2.8\right)+(2 \times 2.8) $
$=14.4\ cm$
Therefore, Area $=12.32\ cm ^2$ and Peri meter $=14.4\ cm$

View full question & answer→

Question 123 Marks

Find the area and perimeter of the following semi-circle :Diameter $= 7$cm

Answer

Diameter $=2 r$
$\Rightarrow r =\frac{\text { diameter }}{2}=\frac{7}{2}=3.5 cm$
Area of the semi-circle $=\frac{1}{2} \pi r^2$
$=\frac{1}{2} \times \frac{22}{7} \times 3.5 \times 3.5 $
$=19.25 cm ^2$
Perimeter of the semi-circle $=(\pi r+2 r)$
$=\left(\frac{22}{7} \times 3.5\right)+(2 \times 3.5)$
$=18\ cm$
Therefore, Area $=19.25 cm ^2$ and Perimeter $=18\ cm$

View full question & answer→

Question 133 Marks

Find the area and perimeter of the following semi-circle :Radius $= 1.4$ cm

Answer

$\text { Area of the semi-circle }=\frac{1}{2} \pi r ^2$
$=\frac{1}{2} \times \frac{22}{7} \times 1.4 \times 1.4 $
$=3.08 cm ^2$
Perimeter of the semi-circle $=(\pi r+2 r)$
$=\left(\frac{22}{7} \times 1 . .4\right)+(2 \times 1.4) $
$=7.2 cm$
Therefore, Area $=3.08 cm ^2$ and Perimeter $=7.2 cm$.

View full question & answer→

Question 143 Marks

Find the area and perimeter of the circle with the following :Radius $= 10.5$ cm

Answer

$\text { Area of the drde }=\pi r^2 $
$=\frac{22}{7} \times 10.5 \times 10.5$
$=346.5 cm ^2$
Peri meter of the circle $=2 \pi r$
$=2 \times \frac{22}{7} \times 10.5 $
$=66 cm$
Therefore, Area $=346.5 cm ^2$ and Perimeter $=66 cm$

View full question & answer→

Question 153 Marks

Find the area and perimeter of the circle with the following :Radius $= 2.8$ cm

Answer

$\text { Area of the cirde }=\pi r^2 $
$=\frac{22}{7} \times 2.8 \times 2.8 $
$=24.64 cm ^2 $
$\text { Perimeter of the circle }=2 \pi r $
$=2 \times \frac{22}{7} \times 2.8 $
$=17.6 cm$
Therefore, Area $=24.64 cm ^2$ and Perimeter $=17.6 cm$

View full question & answer→

Generate Paper Free All Mensuration l topics

[3 marks sum] - Mathematics STD 10 Questions - Vidyadip