Question

A rectangular lawn is 100m long and 45m wide. There are 3 circular ponds, with diameters of 20m, 10m and 5m respectively. Mrs Jones wants to cover the lawn with grass seed. Each packet of grass seed. covers 50m² and costs £1.49 How much will it cost Mrs Jones to cover the lawn with grass seed?​

Answer 1

Given :-

• Length of rectangular lawn = 100m
• Wide of rectangular lawn = 45 m
• Diameter of 3 circular pond = 20m , 10m , 5m

To Find :-

• The cost of covering lawn with grass seed = ?

Solution :-

To calculate the total cost of covering lawn At first calculate the area of lawn and circular ponds then subtract the area of 3 circular pond from the area of rectangular lawn to find out the required area for covering lawn with grass seed.

Calculation for rectangular lawn :-

Length = 100m. Breadth = 45m :-

=> Area = length × breadth

=> Area = 100 × 45

=> Area = 4500m²

Calculation for 3 circular pond :-

• Radius of 1st pond = 20/2 = 10m
• Radius of 2nd pond = 10/2 = 5m
• Radius of 3rd pond = 5/2 = 2.5m

=>Required formula for Area = π r² :-

=> Area of 3 circular pond

=> (π × 10² + π × 5² + π × 2.5²)

=> π × ( 100 + 25 + 6.25)

=> 22/7 × (125 + 6.25)

=> 22/7 × 131.25

=> 2887.5/7

=> 412.5m²

Calculation for required area for covering lawn :-

=> Area of lawn - Area of 3 circular ponds

=> 4500 - 412.5

=> 4087.5m²

=> Required Area = 4087.5/50

=> Required Area = 81.75m²

Calculation for cost of covering lawn :-

=> Total cost = Required area × Rate

• Required Area = 81.75m². Rate =£1.49

=> Total cost = 81.75 × 1.49 = £121.8075

Hence, the cost of covering lawn with grass seed is £121.8075

Answer 2

PROVIDED INFORMATION :-

A rectangular lawn is 100m long and 45m wide. There are 3 circular ponds

diameters of 20m, 10m and 5m respectively

Each packet of grass seed. covers 50m² and costs £1.49

TO FIND :-

How much will it cost Mrs Jones to cover the lawn with grass seed = ?

SOLUTION :-

area of lawn = 45 × 100

= 4500 m

area of these 3 ponds

first ( d = 20, r = 10 m ) = π × 10 ^2 = 314.159

second ( d = 10 , r = 5m ) π × 5 = 78.539 m

third (d = 5, r = 2.5m) π × 2.5 = 19.6349 m

total area of pond = 412.333965 m

remaining area of grass

(4500 - 412.3339 ) = 4087.666 m

cost of 50 m = £1.49

cost 4087.666 m = 1.49/50 ×4087.666

6090.62234/50 £

121.8124£