A cone shaped hat is shown:
A cone is shown with slant height 14 cm and radius 6.2 cm. The unknown height is labeled with a question mark, and the line joining the tip of the cone to the base is perpendicular to the base.
What is the approximate height of the hat? (5 points)
2.79 centimeters, because height = Square root of the difference of 14 and 6.2
4.49 centimeters, because height = Square root of the sum of 14 and 6.2
12.55 centimeters, because height = Square root of the difference of squares of 14 and 6.2
15.31 centimeters, because height = Square root of the sum of the squares of 14 and 6.2
To find the height of the cone, we can use the Pythagorean theorem. The slant height, base radius, and height of the cone form a right-angled triangle.
The height can be found using the equation:
height = √(slant height^2 - base radius^2)
We are given the slant height as 14 cm and the base radius as 6.2 cm.
Plugging in these values, we get:
height = √(14^2 - 6.2^2) = √(196 - 38.44) = √157.56 ≈ 12.55 cm
Therefore, the approximate height of the cone-shaped hat is 12.55 centimeters.
What is the approximate distance between points A and B? (5 points)
A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair 1, 4 is labeled as A, and the ordered pair negative 2, negative 3 is labeled as B.
6.32
6.95
7.62
8.56
To find the distance between two points on a coordinate plane, we can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Given that point A is (1, 4) and point B is (-2, -3), we can plug in these values into the formula:
Distance = √[(-2 - 1)^2 + (-3 - 4)^2] = √[(-3)^2 + (-7)^2] = √[9 + 49] = √58 ≈ 7.62
Therefore, the approximate distance between points A and B is 7.62.
A cylindrical well is 15 meters deep and has a diameter of 1.6 meters. Approximately how many cubic meters of soil were dug out to make the well? (Use π = 3.14.) (5 points)
30.14 cubic meters
37.68 cubic meters
120.57 cubic meters
188.40 cubic meters
To calculate the volume of the soil dug out to make the well, we can use the formula:
Volume = π * (radius^2) * height
Given that the diameter is 1.6 meters, the radius is half of that, which is 0.8 meters. The height of the well is given as 15 meters.
Plugging in these values, we get:
Volume = 3.14 * (0.8^2) * 15 = 3.14 * 0.64 * 15 ≈ 30.14 cubic meters
Therefore, approximately 30.14 cubic meters of soil were dug out to make the well.
The height of a cylinder is 2 units. Its radius is 5 units. What is the volume of the cylinder, in cubic units?
(Use π = 3.14) (5 points)
157 cubic units
314 cubic units
426 cubic units
785 cubic units
To calculate the volume of a cylinder, we use the formula:
Volume = π * (radius^2) * height
Given that the radius is 5 units and the height is 2 units, we can plug these values into the formula:
Volume = 3.14 * (5^2) * 2 = 3.14 * 25 * 2 = 157 cubic units
Therefore, the volume of the cylinder is 157 cubic units.
The tables show some input and output values:
Table A
Input Output
1 7
2 9
3 9
4 5
Table B
Input Output
6 1
7 3
7 2
8 5
Which tables represent functions? (5 points)
Only A
Only B
Both A and B
Neither A nor B
To determine if a table represents a function, we need to check if each input value has a unique corresponding output value.
In Table A, we can see that for each input value, there is only one output value. For example, input 1 corresponds to output 7, input 2 corresponds to output 9, and so on. Therefore, Table A represents a function.
In Table B, we can see that there are duplicate input values. For example, input 7 corresponds to both output 3 and output 2. Since there are multiple output values for a single input value, Table B does not represent a function.
Therefore, only Table A represents a function.