The radius of a circle is 11 miles. What is the circle's area?
2 answers:
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Answer:
The area of the figure is (100 + 50π) cm²
The area of the figure is 257.1 cm² to the nearest tenth
Step-by-step explanation:
<em>The figure is consists of a square with side length 10 cm, and four semi-circles the diameter of each one is equal to the side length of the square</em>
Area of the figure = area of square + 4 × area of a semi-circle
- Area of a square = s², where s is the length of its side
- Area of semi-circle =
πr², where r is the radius of it
∵ The length of the side of the square is 10 cm
∴ s = 10 cm
∵ Area of the square = s²
∴ Area of the square = (10)² = 100
∴ Area of the square is 100 cm²
∵ The diameter of the circle is equal to the side of the square
∴ The diameter of the circle = 10 cm
∵ The radius of a circle is half the diameter of the circle
∴ The radius of the semi-circle = × 10 = 5
∴ The radius of the semi-circle = 5 cm
Now lets find the area of a semi-circle
∵ Area of semi-circle = πr²
∴ Area of semi-circle = π(5)² = 12.5π
∴ Area of each semi-circle is 12.5π cm²
Lets find the area of the figure
∵ Area figure = Area of square + 4 × area of a semi-circle
∴ Area figure = 100 + 4 × 12.5π
∴ Area figure = 100 + 50π
∴ The area of the figure is (100 + 50π) cm²
Substitute π by its value in the calculator
∴ Area figure = 100 + 50(3.141592654)
∴ Area figure = 257.0796327
- Round it to the nearest tenth
∴ The area of the figure is 257.1 cm²
Given:
A right rectangular prism is packed with cubes of side length inch.
Prism is packed with 15 cubes along the length, 6 cubes along the width, and 5 cubes along the height.
To find:
The volume of the prism
Solution:
Side length of each cube inch.
15 cubes along the length, so length of prism is
6 cubes along the width, so width of prism is
5 cubes along the height, so height of prism is
Now,
Volume of rectangular prism is
Therefore, the correct option is B.