Question

the diameter of a 120 cm long roller is 84 cm It takes 1000 complete revolutions in moving once over to level a playground what is the area of the playground​

Answer 1

$\huge\mathtt{\fbox{\red{Answer✍︎}}}$

$\large\underline\mathfrak{\red{GIVEN,}}$

$\sf\dashrightarrow \blue{height(H)= 120cm }$

$\sf\dashrightarrow \blue{diameter of roller= 84cm}$

$\sf\therefore \blue{radius= \dfrac{diameter}{2}}$

$\sf\dashrightarrow \blue{ \dfrac{84}{2}}$

$\sf\dashrightarrow \blue{\cancel \dfrac{84}{2}}$

$\sf\dashrightarrow \blue{radius= 42cm}$

$\large\underline\mathfrak{\purple{TO\:FIND,}}$

$\sf\dashrightarrow \red{AREA\: OF\:PLAYGROUND }$

FORMULA

$\rm{\boxed{\sf{ \circ\:\: C.S.A\: OF\: CYLINDER= 2 \pi rh \:\: \circ}}}$

$\large\underline\mathtt{\purple{SOLUTION,}}$

© ATQ,

$\purple{\text{AREA COVERED BY ROLLER IN 1 REVOLUTION = PERIMETER OF ROLLER}}$

$\sf\therefore \pink{AREA \:COVERED \:IN\: ONE\: REVOLUTION= 2 \pi r h}$

$\sf\implies \red{ 2 \times \dfrac{22}{7} \times 42 \times 120}$

$\sf\implies \blue{ 2 \times \dfrac{22}{\cancel{7}} \times \cancel{42} \times 120}$

$\sf\implies \red{2 \times 22 \times 6 \times 120}$

$\sf\implies \blue{ 44 \times 72 }$

$\sf\implies \pink{ 31680cm^2 }$

$\rm{\boxed{\sf{ \circ\:\: 31680cm^2\:\: \circ}}}$

$\sf\therefore \purple{ THE\:ROLLER\:TAKES\:1000\: REVOLUTIONS TO\:COVER\:AREA\:OF\:THAT\: PARTICULAR\:PALAYGROUND}$

$\sf\therefore \blue{we\: know,\: to\: complete\: one \:revolution\: it \:takes \:31680cm^2 \:area }$

$\sf\therefore \red{then \:area \:of\:rectangle = 1000 \times the \:area\: in\: one\: complete\: revolution}$

$\sf\implies \pink{ 1000 \times 31680 }$

$\sf\implies \green{31680000cm^2}$

CONVERSION,

$\sf\therefore \green{cm^2 \:into\:m^2}$

$\sf\therefore \blue{\dfrac{ 31680000}{ 100 \times 100}}$

$\sf\implies \red{\cancel \dfrac{ 31680000}{ 100 \times 100}}$

$\sf\implies \orange{3168 m^2}$

$\rm{\boxed{\sf{ \circ\:\: AREA\:OF\: PLAYGROUND= 3168m^2 \:\: \circ}}}$

$\rm\underline\mathrm{AREA\:OF\:PLAYGROUND\:IS\:3168cm^2}$

Answer 2

Explanation:

Area of triangle is 5400 m².

Step-by-step explanation:

Given:-

Sides of triangle are in ratio 3:4:5.

Perimeter of triangle is 360 m.

To find:-

Area of triangle.

Solution:-

Let, Sides of triangle be 3x, 4x and 5x.

Perimeter of triangle = a+b+c

Where, a,b and c are sides of triangle.

Puting sides and perimeter of triangle.

\longrightarrow⟶ 3x + 4x + 5x = 360

\longrightarrow⟶ 12x = 360

\longrightarrow⟶ x = 360/12

\longrightarrow⟶ x = 30

Sides of triangle :-

3x = 3×30 = 90

4x = 4×30 = 120

5x = 5×30 = 150

Sides of triangle are 90m, 120m and 150m.

Area of triangle by using Heron's formula is :

Area of triangle = \bold{\sqrt{s(s-a)(s-b)(s-c)}}

s(s−a)(s−b)(s−c)

Where,

S is semi-perimeter of triangle.

a, b and c are sides of triangle.

So,

Semi-perimeter = Perimeter/2

= 360/2

= 180

Semi-perimeter of triangle is 180 m.

Area of triangle:

\longrightarrow⟶ √180(180 - 90)(180 - 60)(180 - 30)

\longrightarrow⟶ √180 × 90 × 60 × 30

\longrightarrow⟶ √29160000

\longrightarrow \purple{\boxed{\sf \bold{ 5400}} \star}⟶

5400

⋆

Therefore,

Area of triangle is 5400 m².