Question

a gardener is designing a circular garden. On the blueprint, the garden has a diameter of 16 centimeters. The blueprint has a scale of two centimeters to five feet. What will be the actual area of the garden, in square feet, after it is built? Round your answer to the nearest tenth of a square foot.

Answer 1

The actual area of the garden is 1256 square feet.

Explanation:

Given:

A gardener is designing a circular garden.

On the blueprint, the garden has a diameter of 16 centimeters.

The blueprint has a scale of two centimeters to five feet.

Now, to find the actual area of the garden.

Let the actual diameter of the garden be
`x\ feet.`

And the diameter of the garden on blueprint =
`16\ centimeters.`

As, given:

The blueprint has a scale of two centimeters to five feet.

2 centimeters is equivalent to 5 feet.

Thus, 16 centimeters is equivalent to
`x\ feet.`

Now, to get the actual diameter by using cross multiplication method:

`(2)/(5) =(16)/(x)`

By cross multiplying we get:

`2x=80`

Dividing both sides by 2 we get:

`x=40\ feet.`

Thus, the actual diameter of the garden is 40 feet.

Now, to get the area of the garden we get the radius and then put the formula of area:

Radius =
`(Diameter)/(2)`

Radius(r)=
`(40)/(2)=20\ feet.`

`Area =\pi r^2.`

`Area=3.14* 20^2`

`Area=3.14* 400`

`Area=1256\ square\ feet.`

Therefore, the actual area of the garden is 1256 square feet.