1. What does lateral area mean? *
1 point
the surface area of a whole solid
the surface area of the bases of a solid
the surface area minus the base(s)
The correct answer is the surface area minus the base(s). Lateral area refers to the surface area of a solid that does not include the base(s).
2. Find the surface area of a square pyramid with a base length of 3 ft and a slant height of 8 ft. *
1 point
63 ft^2
57 ft^2
48 ft^2
72 ft^2
To find the surface area of a square pyramid, we need to calculate the sum of the areas of the base and the four triangular faces.
The base of the square pyramid is a square with a side length of 3 ft, so the area of the base is 3 ft * 3 ft = 9 ft^2.
Each triangular face of the pyramid is an isosceles triangle, with the slant height as one side, the height as the other side, and the base length as the base.
The height of the triangular face can be found using the Pythagorean theorem:
height^2 + (base length / 2)^2 = slant height^2
height^2 + (3 ft / 2)^2 = 8 ft^2
height^2 + 2.25 ft^2 = 64 ft^2
height^2 = 61.75 ft^2
height ≈ 7.84 ft
The area of each triangular face can be calculated as (base length * height) / 2.
Area of each triangular face = (3 ft * 7.84 ft) / 2 ≈ 11.76 ft^2
Since the square pyramid has four triangular faces, the total surface area (including the base) is:
Total surface area = base area + 4 * triangular face area
Total surface area = 9 ft^2 + 4 * 11.76 ft^2
Total surface area = 9 ft^2 + 47.04 ft^2
Total surface area ≈ 56.04 ft^2
Therefore, the surface area of the square pyramid is approximately 56.04 ft^2.
The closest option is given as 57 ft^2.
. Find the volume of the rectangular prism. Round to the nearest tenth.
*
1 point
L=7 H=4 W=5
280 cm^3
112 cm^3
140 cm^3
132 cm^3
To find the volume of a rectangular prism, we multiply the length by the height, and then multiply that result by the width.
Given:
Length (L) = 7 cm
Height (H) = 4 cm
Width (W) = 5 cm
Volume = L * H * W
Volume = 7 cm * 4 cm * 5 cm
Volume = 140 cm^3
Therefore, the volume of the rectangular prism is 140 cm^3. The closest option is given as 140 cm^3.