Question

The diameter of a 2 m long roller is 50 cm if it takes 400 revolution to level a playground find the cost of levelling at the rate of 85 paisa per square
please answer ​

Answer 1

Answer:

$\bigstar{\bold{Cost\:of\:levelling=1067.6\:rupees}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Diameter = 50 cm = 0.5 m
• Height = 2m
• Cost of levelling = 85 paisa per m² = 0.85 rupees per m²

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Cost of levelling

$\Large{\underline{\underline{\bf{Solution:}}}}$

➥ First we have to find the area levelled by the roller.

➥ Here,

    Area levelled by the roller in one revolution = CSA of the cylindrical roller

➥ CSA of a cylinder is given by,

    CSA of a cylinder = 2 π r h

➥ Substitute the data,

    CSA of the cylinder = 2 × 3.14 × 0.5/2 × 2

    CSA of the cylinder = 3.14 × 0.5 × 2

    CSA of the cylinder = 3.14 m²

➥ Hence area levelled in one revolution by the roller = 3.14 m²

➥ Area levelled in 400 revolutions = 3.14 × 400

    Area levelled in 400 revolutions = 1256 m²

➥ Hence total area levelled by the roller is 1256 m²

➥ Now the cost of levelling is given by,

   Cost of levelling = 0.85 × 1256

   Cost of levelling = 1067.6 rupees

➥ Hence the cost of levelling is 1067.6 rupees

    $\boxed{\bold{Cost\:of\:levelling=1067.6\:rupees}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

➥ The curved surface area of cylinder is given by,

    CSA of cylinder = 2 π r h

➥ The total surface area of cylinder is given by,

    TSA of cylinder = 2 π r (r + h)

➥ Volume of a cylinder is given by,

    Volume of cylinder = π r² h