Chapter 6: Q. 95 (page 366)

A water sprinkler sprays water over a distance of $30$ feet while rotating through an angle of $135^{\circ}$

Short Answer

Expert verified

The area of the lawn that receives the water from the sprinkler is $1060.29 f t^{2}$

Step by step solution

Step 1. Given information

water sprinkler sprays water over a distance of $30$ feet while rotating through an angle of $135^{\circ}$

Step 2. Used formulae

The area of a circle with radius $r$ and angle $θ$ is $A = \frac{1}{2} r^{2} θ$

Step 3. Calculation

$135^{\circ} = 135 \cdot \frac{π}{180} = \frac{3 π}{4}$

For the given problem, we substitute and the area is obtained as

$A = \frac{1}{2} \cdot {(30)}^{2} \cdot \frac{3 π}{4} = 90 π \approx 1060.29 f t^{2}$

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A water sprinkler sprays water over a distance of $30$ feet while rotating through an angle of $135^{\circ}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Used formulae

Step 3. Calculation

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A water sprinkler sprays water over a distance of 30feet while rotating through an angle of135∘

Short Answer

Step by step solution

Step 1. Given information

Step 2. Used formulae

Step 3. Calculation

One App. One Place for Learning.

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A water sprinkler sprays water over a distance of $30$ feet while rotating through an angle of $135^{\circ}$