Question

A roller 150 cm long has a diameter of 70 cm. To level a playground it takes 750 complete revolutions. Determine the cost of leveling the playground at the rate of 75 paise per square. meter

Answer 1

Area of playground = 750 × CSA of roller
= 750 × 2 × 22÷7 × 35 × 150
= 750 × 33000
= 24750000 cm^2
= 2475 m^2
Cost of leveling = 2475 × 0.75
= Rs 1856.25

Answer 2

The cost of leveling the playground at the rate of 75 paise per square meter is 1856.25 Rs.

Given: A roller

• 150 cm long has a
• Diameter 70 cm.
• To level a playground it takes 750 complete revolutions.

To find:

Determine the cost of leveling the playground at the rate of 75 paise per square meter.

Solution:

Concept used: 1 revolution of cylindrical roller is equal to curved surface area of roller.

Formula used:

$\bf CSA = 2\pi \: rh$

where,

r: radius of cylinder

h: height/length of cylinder

Step 1: Find CSA of roller.

It is given that

Diameter: 70 cm

and 2r=d=70 cm

Length(h)=150 cm

$CSA = \frac{22}{7} \times 70 \times 150$

$CSA = 22 \times 10 \times 150$

$CSA = 33000 \: {cm}^{2}$

Step 2: Find total area of ground.

Area of total ground can be calculated by multiplying CSA with number of revolution.

Area of ground

$= 750 \times 33,000 \: {cm}^{2}$

$= 24,750,000\: {cm}^{2}$

or

Area of ground$\bf = 2475 \: {m}^{2}$

(As 1 meter²= 10000 cm²)

Step 3: Find cost of leveling.

As cost of leveling is 75 paise per m².

So,

Total cost $= 75 \times 2475 \: paise$

$= 185625 \: paise$

or

Total cost$\bf = 1856.25 \: rupees$

(as 1 rupees= 100 paise)

Therefore,

The cost of leveling the playground at the rate of 75 paise per square meter is 1856.25 Rs.

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