Use Euler’s formula to find the missing number.
Vertices: 10
Edges: 29
Faces: ?
(1 point)
Responses
22
22
21
21
24
24
20
The formula is: V - E + F = 2
Given:
V = 10
E = 29
F = ?
10 - 29 + F = 2
-19 + F = 2
F = 2 + 19
F = 21
Therefore, the missing number of faces is 21.
Correct response: 21
Describe the cross section.
The figure shows a cube with a rectangle that slices through the four side faces.
The rectangle slices through the back left edge of the cube through the back face and left face, then through the front left edge and back right edge so that it finishes outside the front and right faces of the cube.
The shaded cross section has an edge on the left face, an edge on the back face, an edge from the back face to the right face, an edge on the right face, an edge on the front face, and an edge between the left face and right face.
(1 point)
Responses
pentagon
pentagon
trapezoid
trapezoid
hexagon
hexagon
cube
hexagon
What is the lateral area of a regular pentagonal pyramid that has a slant height of 18 in. and a base side length of 9 in.?
(1 point)
Responses
405 in.2
405 in. 2
810 in.2
810 in. 2
81 in.2
81 in. 2
162 in.2
To find the lateral area of a regular pentagonal pyramid, we use the formula:
Lateral Area = (1/2) * Perimeter of Base * Slant Height
The perimeter of the base of a regular pentagon can be found by multiplying the side length by 5:
Perimeter = 5 * 9 = 45 in
Now, calculate the lateral area:
Lateral Area = (1/2) * 45 * 18
Lateral Area = 405 in^2
Therefore, the lateral area of the regular pentagonal pyramid is 405 in^2.
Correct response: 405 in.2
What is the volume of the given prism? Round the answer to the nearest tenth.
A triangular prism is shown. The sides of the triangular base are labeled 18 yards, 18 yards, and 18 yards. The edge of the prism connecting the two bases is labeled 35 yards.
(1 point)
Responses
11,340.0 yd3
11,340.0 yd 3
9,820.7 yd3
9,820.7 yd 3
4,910.4 yd3
4,910.4 yd 3
2,170.6 yd3
To find the volume of the triangular prism, we use the formula:
Volume = (1/2) * base * height * depth
Given:
Base side of the triangle = 18 yards
Height of the triangle (corresponds to the edge of the prism) = 35 yards
Depth of the prism = 18 yards
Now, calculate the volume:
Volume = (1/2) * 18 * 35 * 18
Volume = 11,340 yd^3
Therefore, the volume of the given prism is 11,340.0 yd^3.
Correct response: 11,340.0 yd3
What is the height of the cylinder? The figure is not drawn to scale.
a cylinder
(1 point)
Responses
18 in
18 in
11.3 in
11.3 in
7.2 in
7.2 in
3.6 in
Without the figure to reference, I will assume information from the options provided. Since the question asks for the height of the cylinder, we can directly obtain the value from the answer choices.
The height of the cylinder is 18 in.
Correct response: 18 in