2. Write 5 2/3% as a decimal. a. 5.3 b. 0.056 c. 0.56 d. 566.6
2 answers:
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First, illustrate the problem by drawing a square inside a circle as shown in the first picture. Connect each corner of the square to the center of the circle. Since the square is inscribed in the circle, they have the same center points. Each segment drawn to the corners is a radius of the circle measuring 1 unit. Also, a square has equal sides. So, the angle made between those segments are equal. You can determine each angle by dividing the whole revolution into 4. Thus, each point is 360°/4 = 90°.
Next, cut a portion of one triangle from the circle as shown in the second picture. Since one of the angles is 90°, this is a right triangle with s as the hypotenuse. Applying the pythagorean theorem,
s = √(1²+1²) = √2
So each side of the square is √2 units. The area of the square is, therefore,
A = s² = (√2)² = 2
The area of the square is 2 square units.
Next, cut a portion of one triangle from the circle as shown in the second picture. Since one of the angles is 90°, this is a right triangle with s as the hypotenuse. Applying the pythagorean theorem,
s = √(1²+1²) = √2
So each side of the square is √2 units. The area of the square is, therefore,
A = s² = (√2)² = 2
The area of the square is 2 square units.
The volume of the composite figure is 263.76 inches³
Step-by-step explanation:
The volume of a cylinder of radius r and height h is
- V = πr²h ⇒ Bh
The volume of a cone of radius r and height h is
- V =
πr²h ⇒
The volume of a sphere with radius r is
- V =
πr³
∵ The figure is made up of a cylinder, a cone, and a half sphere
∵ The radius of the cylinder = 3 inches
∵ The height of the cylinder = 6 inches
∵ π = 3.14
- Use the rule of the volume of the cylinder above
∴ The volume of the cylinder = (3.14)(3)²(6)
∴ The volume of the cylinder = 169.56 inches³
∵ The radius of the cone = 3 inches
∵ The height of the cone = 4 inches
∵ π = 3.14
- Use the rule of the volume of the cone above
∴ The volume of the cone =
∴ The volume of the cone = 37.68 inches³
∵ The radius of the half sphere = 3 inches
∵ π = 3.14
- Use the rule of the volume of the sphere above to find the
volume of the half sphere
∴ The volume of half sphere =
∴ The volume of half sphere = 56.52 inches³
To find the volume of the composite figure add the volumes of the three shapes above
∵ The volume of the composite figure = 169.56 + 37.68 + 56.52
∴ The volume of the composite figure = 263.76 inches³
The volume of the composite figure is 263.76 inches³
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