In a right circular cylinder, the lateral surface meets the base at a right angle if the height and radius are perpendicular to each other.
In Model 2, the height is 35 cm and the radius is 6 cm. These dimensions are not perpendicular to each other.
In Model 3, the height is 40 cm and the radius is 20 cm. These dimensions are not perpendicular to each other.
In Model 4, the height is 9 cm and the radius is 24 cm. These dimensions are not perpendicular to each other.
Therefore, the lateral surface of Model 1 meets the base at a right angle.
Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in the table.
A cylinder.
Model 1
radius: 14 cm
height: 48 cm
diagonal: 50 cm
Model 2
radius: 6 cm
height: 35 cm
diagonal: 37 cm
Model 3
radius: 20 cm
height: 40 cm
diagonal: 60 cm
Model 4
radius: 24 cm
height: 9 cm
diagonal: 30 cm
In which model does the lateral surface meet the base at a right angle?
Model 1
Model 2
Model 3
Model 4
9 answers
Angelica calculated the distance between the two points shown on the graph below.
On a coordinate plane, line A B has points (2, negative 5) and (negative 4, 5).
Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.
Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.
Step 3: Substitute the values into the Pythagorean theorem: 10 squared = 6 squared + c squared.
Step 4: Evaluate 10 squared = 6 squared + c squared. 100 = 36 + c squared. 64 = c squared. 8 = c.
She states the length of AB is 8 units. Which best describes the accuracy of Angelica’s solution?
Angelica is correct.
Angelica made an error determining the location of the right angle. The right angle should be at (2, 5).
Angelica made an error counting the lengths of the legs of the right triangle. The lengths should be 7 and 11.
Angelica made an error substituting the values into the Pythagorean theorem. The equation should be c squared = 6 squared + 10 squared.
On a coordinate plane, line A B has points (2, negative 5) and (negative 4, 5).
Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.
Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.
Step 3: Substitute the values into the Pythagorean theorem: 10 squared = 6 squared + c squared.
Step 4: Evaluate 10 squared = 6 squared + c squared. 100 = 36 + c squared. 64 = c squared. 8 = c.
She states the length of AB is 8 units. Which best describes the accuracy of Angelica’s solution?
Angelica is correct.
Angelica made an error determining the location of the right angle. The right angle should be at (2, 5).
Angelica made an error counting the lengths of the legs of the right triangle. The lengths should be 7 and 11.
Angelica made an error substituting the values into the Pythagorean theorem. The equation should be c squared = 6 squared + 10 squared.
Angelica made an error determining the location of the right angle. The right angle should be at (2, 5).
To find the length of AB, we need to calculate the distance between points (2, -5) and (-4, 5).
Using the distance formula, the length of AB is calculated as follows:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-4 - 2)^2 + (5 - (-5))^2) = sqrt((-6)^2 + (10)^2) = sqrt(36 + 100) = sqrt(136).
Therefore, Angelica's solution is incorrect and the length of AB is sqrt(136) units, not 8 units.
To find the length of AB, we need to calculate the distance between points (2, -5) and (-4, 5).
Using the distance formula, the length of AB is calculated as follows:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-4 - 2)^2 + (5 - (-5))^2) = sqrt((-6)^2 + (10)^2) = sqrt(36 + 100) = sqrt(136).
Therefore, Angelica's solution is incorrect and the length of AB is sqrt(136) units, not 8 units.
What is the length of segment AC?
On a coordinate plane, line A C has points (3, negative 1) and (negative 5, 5).
On a coordinate plane, line A C has points (3, negative 1) and (negative 5, 5).
To find the length of AC, we can use the distance formula.
The distance formula is given by:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So in this case, the length of AC is:
AC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-5 - 3)^2 + (5 - (-1))^2)
= sqrt((-8)^2 + (5 + 1)^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
Therefore, the length of segment AC is 10 units.
The distance formula is given by:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So in this case, the length of AC is:
AC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-5 - 3)^2 + (5 - (-1))^2)
= sqrt((-8)^2 + (5 + 1)^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
Therefore, the length of segment AC is 10 units.
What is the length of segment XY?
On a coordinate plane, line X Y has points (negative 4, 0) and (3, 2).
4.5 units
StartRoot 45 EndRoot units
StartRoot 53 EndRoot units
9 units
On a coordinate plane, line X Y has points (negative 4, 0) and (3, 2).
4.5 units
StartRoot 45 EndRoot units
StartRoot 53 EndRoot units
9 units
To find the length of XY, we can use the distance formula.
The distance formula is given by:
XY = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So in this case, the length of XY is:
XY = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((3 - (-4))^2 + (2 - 0)^2)
= sqrt((7)^2 + (2)^2)
= sqrt(49 + 4)
= sqrt(53)
Therefore, the length of segment XY is sqrt(53) units.
The distance formula is given by:
XY = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So in this case, the length of XY is:
XY = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((3 - (-4))^2 + (2 - 0)^2)
= sqrt((7)^2 + (2)^2)
= sqrt(49 + 4)
= sqrt(53)
Therefore, the length of segment XY is sqrt(53) units.
Which equation correctly shows how to determine the distance between the points (9, –2) and (6, 3) on a coordinate grid?
d = StartRoot (6 minus 3) squared + (9 minus (negative 2)) squared EndRoot
d = StartRoot (6 + 3) squared + (9 + (negative 2)) squared EndRoot
d = StartRoot (6 minus 9) squared + (3 minus (negative 2)) squared EndRoot
d = StartRoot (6 + 9) squared + (3 + (negative 2)) squared EndRoot
d = StartRoot (6 minus 3) squared + (9 minus (negative 2)) squared EndRoot
d = StartRoot (6 + 3) squared + (9 + (negative 2)) squared EndRoot
d = StartRoot (6 minus 9) squared + (3 minus (negative 2)) squared EndRoot
d = StartRoot (6 + 9) squared + (3 + (negative 2)) squared EndRoot
The correct equation to determine the distance between the points (9, -2) and (6, 3) on a coordinate grid is:
d = sqrt((6 - 9)^2 + (3 - (-2))^2)
This equation represents the distance formula, which calculates the distance between two points in a Cartesian coordinate system.
d = sqrt((6 - 9)^2 + (3 - (-2))^2)
This equation represents the distance formula, which calculates the distance between two points in a Cartesian coordinate system.
1 answer