Important Questions for Mensurations Class 8 Maths

$C= 2 \pi r$ and $A= \pi r^2$

(a) r=21 cm , $C=2 \pi r= 132 \ cm$ , $A= \pi r^2= 1386 \ cm^2$
(b) r=6.3 cm , $C=2 \pi r= 39.6 \ cm$ , $A= \pi r^2= 124.74 \ cm^2$
(c)r=14 mm , $C=2 \pi r= 88 \ mm$ , $A= \pi r^2= 616 \ m^2$
(d) r=28 cm , $C=2 \pi r= 176 \ cm$ , $A= \pi r^2= 2464 \ cm^2$
(e) r=49 cm , $C=2 \pi r= 308 \ cm$ , $A= \pi r^2= 7546 \ cm^2$
(f) r=77 mm , $C=2 \pi r= 484 \ mm$ , $A= \pi r^2= 18634 \ mm^2$

Here C=176 m or $2 \pi r =176$ or r=28 m
D= 2r= 56 cm
$A= \pi r^2= 2464 \ cm^2$

Here A=616 cm²
or
$\pi r^2= 616$ or r=14 cm
D=2r = 28 cm
C=88 cm

Area of remaining sheet is the difference in the area of 5 cm circle and 3 cm circle
$A= \pi (5)^2 - \pi (3)^= 50.28 \ cm^2$

Perimeter = Half Circumference of circle of radius 5 cm + Diameter of the circle $=\pi \times 5 + 10=25.7 \ cm$

Circumference of wheel = 2 π r = 2 π (35) = 220 cm
Now Wheel moves 220 cm in 1 round
then it will move 110m in (11000/220)=50 rounds

We have $\frac {r_1}{r_2} = \frac {3}{2}$
$\frac {C_1}{C_2} = \frac {2 \pi r_1}{2 \pi r_2} = \frac {r_1}{r_2} = \frac {3}{2}$

Radius of Outer Circle=Circumference/2π= 616/2 π = 98 cm
Radius of the inner circle= Diameter/2 = 150/2= 75 cm
The width of the parapet= 98-75=23 cm

Length of thin wire= Perimeter of equilateral triangle= 3 × 11= 33 cm
Now
Radius of the circle= Circumference/2π = 33/2 π = 5.25 cm
Area of circle = π r² = 86.625 cm²

Perimeter of Square = 88 cm
Now
Radius of the circle= Circumference/2π = 88/2 π = 14 cm
Area of circle = π r² = 616 cm²

$\frac {A_1}{A_2} = \frac {16}{121}$
$\frac { \pi r_1^2}{\pi r_2^2}= \frac {16}{121}$
$\frac {r_1}{r_2} = \frac {4}{11}$
Now
$\frac {C_1}{C_2} = \frac {2 \pi r_1}{2 \pi r_2}=\frac {r_1}{r_2} = \frac {4}{11}$
$\frac {D_1}{D_2} = \frac {2 r_1}{2 r_2}=\frac {r_1}{r_2} = \frac {4}{11}$

circumference of a wheel= 2 π r = 2 π (49) = 308 cm
Distance covered in 1 round= circumference of a wheel
Wheel covers 5 revolutions in 1 sec
So , it does 600 revolutions in 120 sec
Now Distance covered in 1 round is 308 cm
Then Distance covered in 600 round will be 308 × 600 = 184800 cm = 1848 m

Circumference=2 π r = 2 π (63) = 396 cm
Distance covered in 1 round= circumference of a wheel
So total turns required = 158400/396=400 turns