Draw and label a diagram of each figure described below and calculate its volume.
A) a sphere with a radius of 2 m.
B) a cone with a diameter of 8 ft and height of 10 feet.
(4/3) pi r^3 = (4/3)pi(8) = 33.51 m^3
(1/3)(pi)(4)^2 (10) = 167.6 m^3
Draw and label the figure described
To draw and label a diagram of each figure, follow the step-by-step instructions below:
A) A sphere with a radius of 2 m:
1. Take a sheet of paper and a pencil.
2. Draw a dot in the center of the paper. This will represent the center of the sphere.
3. Measure and mark a point 2 cm to the right and left of the center dot. These points will represent the edges of the sphere.
4. Use a compass or a round object to draw a circle passing through the three marked points.
5. Label the circle as the sphere and write "Radius = 2 m" near it.
B) A cone with a diameter of 8 ft and height of 10 ft:
1. Place the paper horizontally to draw the diagram.
2. Draw a vertical line in the middle of the paper. This will represent the axis of the cone.
3. Measure and mark two points 4 ft above and below the center of the line. Label these points as the top and bottom of the cone.
4. From the top point, draw a curved line connecting the top to the bottom point. The curve should be wider at the bottom, forming the shape of a cone.
5. Measure and mark a point in the middle of the line connecting the top and bottom points. This will represent the center of the base of the cone.
6. Use a compass to draw a circle with a diameter of 8 ft using the marked center point.
7. Label the circle as the base of the cone and write "Diameter = 8 ft" near it.
8. Draw a diagonal line from the apex of the cone to the circumference of the base, representing the slant height of the cone.
9. Measure and label the height of the cone as 10 ft.
To calculate the volume of each figure:
A) The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * r^3,
where r is the radius of the sphere (which is 2 m in this case).
Plug the value of r into the formula:
Volume = (4/3) * π * (2 m)^3 = (4/3) * π * 8 m^3 ≈ 33.51 m^3
Therefore, the volume of the sphere is approximately 33.51 cubic meters.
B) The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r^2 * h,
where r is the radius of the base and h is the height of the cone.
Since the diameter of the base is given (which is 8 ft), we need to divide it by 2 to find the radius.
The radius (r) is 8 ft / 2 = 4 ft.
Plug the values of r and h into the formula:
Volume = (1/3) * π * (4 ft)^2 * 10 ft = (1/3) * π * 16 ft^2 * 10 ft ≈ 167.55 ft^3
Therefore, the volume of the cone is approximately 167.55 cubic feet.