Question

solve the above question...​

Answer 1

$\mathfrak{\huge{\underline{Solution:}}}$

$\textbf{\huge{\underline{Given:}}}$

● Diameter = 84cm

● Height = 120 cm

● Area of playground = 1584m^2

__________________________

$\star$ Area of roller = C.S.A of cylinder

$\star \rm \: C.S.A = 2 \: \pi \: r \: h$

$\hookrightarrow \sf \: 2 \times \dfrac{22}{ 7} \times42 \times 120$

$\hookrightarrow \sf \large \boxed{31680 \sf \: {m}^{2} }$

$\textbf{\underline{\underline{Area\:to\:be\:covered:}}}$

$\hookrightarrow \sf \: 1584 \times 10000$

$\hookrightarrow \large \sf \boxed{15840000 \sf \: {cm}^{2} }$

$\textbf{\underline{\underline{Total\:No.\:of\:revolutions:}}}$

$\hookrightarrow \sf \cancel\dfrac{15840000}{31680}$

$\hookrightarrow \sf \large \boxed{500 \sf \: revolutions}$

Answer 2

$\bf{\Huge{\underline{\boxed{\rm{\red{ANSWER\::}}}}}}$

Given:

Diameter & length of a roller are 84cm and 120cm respectively.

$\bf{\Large{\underline{\sf{\green{To\:find\::}}}}}$

The revolution can the roller level the playground of area 1584m².

$\bf{\Large{\underline{\sf{\pink{Explanation\::}}}}}$

We have,

$\bf\begin{cases}\sf{Diameter=84cm}\\ \sf{Length\:of\:roller=120cm}\\ \sf{Area\:of\:playground=1584m^{2}}\end{cases}$

→ Radius of the roller= $\frac{84}{2}cm$

→ Radius of the roller= 42cm.

• When a wheel roller rotates completely,it cover certain distance.
• If roller moves in whole playground.

We know that formula of the curved surface area of cylinder: 2πrh

We know that; $\boxed{1m=100cm\\&1cm=\frac{1}{100} m}}$

• Radius of the roller= 0.42m
• Length of the roller= 1.2m

Now,

Area of playground=Curved surface area of roller×Number of revolutions

• Curved surface area of roller:

⇒ 2πrh  [sq.units]

⇒ $(2*\frac{22}{7} *0.42*1.2)m^{2}$

⇒ $(\frac{44}{\cancel{7}} *\cancel{0.42}*1.2)m^{2}$

⇒ (44× 0.06× 1.2)m²

⇒ 3.168m²

Therefore,

→ Area of playground = curved surface area of roller ×No. of revolutions

→ 1584m² = 3.168m² × Number of revolutions

→ Number of revolutions= $\frac{1584*1000m^{2} }{3.168*1000m^{2} }$

→ Number of revolutions= $\cancel{\frac{1584000m^{2} }{3168m^{2} } }$

→ Number of revolutions = 500.