6.04 Area of a circle
Find the area of the following circles to one decimal place:
Find the area of the following circles, correct to one decimal place.
A circle of radius 5\text{ in}.
A circle of diameter 8\text{ in}
Calculate the exact area of the following circles:
A circle has a radius of 4 \, \text{yd}.
A circle has a diameter of 8 \,\text{ft}.
A circle has a radius of 12 \, \text{ft}.
The area of a circle is 418\text{ yd}^{2}.
If its radius is r\text{ yd}, find r, correct to two decimal places.
Now find the circumference of the circle. Round your answer to one decimal place.
For each of the following circles:
Calculate the radius.
Hence, calculate the exact area.
A circle with diameter of 12 \,\text{in}.
A circle with circumference of 14 \pi \,\text{ft}.
A circle with circumference of 18 \,\text{yd}.
A circle with diameter of 22 \,\text{mm}.
Find the shaded area of the following figures, correct to one decimal place:
Find the area of the following shapes to one decimal place:
The radius of a circular baking tray is 10 \text{ cm}. Find its area, correct to two decimal places.
A wind turbine has blades that are R\text{ m} long which are attached to a tower 60\text{ m} high. When a blade is at its lowest point (pointing straight down), the distance between the tip of the blade and the ground is 20\text{ m}.
Calculate the value of R.
Find the distance travelled by the tip of the blade during one full revolution, correct to two decimal places.
A factor in the design of wind turbines is the amount of area covered by their blades. The larger the area covered, the more air can pass through the blades.
Find the area inside the circle defined by the rotation of the blade tips, correct to two decimal places.
The engineering team at Rocket Surgery are building a rocket for an upcoming Mars mission.
A critical piece is the circular connective disk that connects the booster rocket to the rest of the spacecraft. This disk must completely cover the top of the booster rocket.
The booster rocket has a diameter of precisely 713.5 centimeters. Answer the following correct to two decimal places.
Find the required area of the connective disk.
Instead of using the exact value, an engineer uses the approximation 3.14 for \pi.
Find the area using the engineer's approximation for \pi.
If the connective disk is more than 100 \,\text{cm}^2 too small, the disk will malfunction, resulting in catastrophic launch failure.
Will the disk malfunction if it is built according to the engineer's calculation? Explain your answer.