Question

end-of-unit assessment (a)
a circle has a radius of 10 cm. what is the closest to its area?
a. 157 cm²
b. 314 cm²
c. 3.144 cm²
d. 15.708 cm²
the shape is composed of three squares and two semicircles. select all the expressions that correctly calculate the perimeter of the shape.
a. 40 + 20π
b. 80 + 20π
c. 120 + 20π
d. 300 + 100π
e. 10 + 10 + 10π + 10 + 10 + 10π

Explanation:

Step1: Analyze the perimeter of the shape

The side - length of each square is \(10\).
The straight - line parts of the perimeter: There are \(4\) sides of length \(10\).
The curved parts: There are two semicircles. The diameter of each semicircle is \(10\). The formula for the circumference of a circle is \(C = \pi d\). The two semicircles together form a full circle with diameter \(d = 10\), so the length of the curved part is \(\pi\times10\).

Step2: Calculate the perimeter

The sum of the straight - line parts: \(4\times10=40\).
The sum of the curved parts: \(\pi\times10+\pi\times10 = 20\pi\).
The perimeter \(P=40 + 20\pi\).
Also, \(10+10 + 10\pi+10 + 10+10\pi=(10 + 10+10 + 10)+(10\pi+10\pi)=40 + 20\pi\)

Answer:

A. \(40 + 20\pi\), E. \(10 + 10+10\pi+10 + 10+10\pi\)