use the image to answer the question
An illustration shows two cubes joined on both sides of a cuboid. The sides of the cube are 2 yards. The length of the cuboid is 4.5 yards.
what is the volume of the composite figure?
__ yd.^3
To find the volume of the composite figure, we need to find the volume of each individual figure and then add them together.
Volume of the two cubes:
Each cube has a side length of 2 yards, so the volume of each cube is 2^3 = 8 cubic yards. Since there are two cubes, the total volume of the cubes is 8 + 8 = 16 cubic yards.
Volume of the cuboid:
The length of the cuboid is given as 4.5 yards. Since the cuboid is made up of two cubes attached to it, the width and height of the cuboid are the same as the side length of the cubes, which is 2 yards. Therefore, the volume of the cuboid is 4.5 x 2 x 2 = 18 cubic yards.
Total volume of the composite figure:
To find the total volume, we need to add the volume of the cubes to the volume of the cuboid: 16 + 18 = 34 cubic yards.
Therefore, the volume of the composite figure is 34 cubic yards.
use the image to answer the question.
An illustration shows a hexagonal prism with the label Choosy Cheesy on the top surface. The height of the hexagonal prism is 8 centimeters. The two longer parallel sides of the hexagonal prism each measure 30 centimeters in length. One end of the prism is marked with a dashed line measuring 15 centimeters across, joining the two opposite vertices of the parallel edges, forming a triangular prism with a perpendicular measure of 8 centimeters.
a sample of gourmet cheeses came in this box. what is the volume of the box?
__ cm^3
To determine the volume of the box, we first need to find the volumes of each separate figure and then add them up to get the total volume.
1. Volume of the hexagonal prism:
The formula to find the volume of a prism is V = base area x height. Since the base of the hexagonal prism is a hexagon, we need to calculate the area of the hexagon first. The formula for the area of a regular hexagon is A = (3√3 x side length squared)/2.
In this case, the side length of the hexagon is 30 cm, so the area of the base hexagon is A = (3√3 x 30^2)/2 ≈ 779 cm^2.
Now, we can find the volume of the hexagonal prism:
V_hexagon_prism = 779 cm^2 x 8 cm = 6232 cm^3
2. Volume of the triangular prism:
The formula for the volume of a triangular prism is V = (1/2) x base area x height. The base of the triangular prism is a triangle with a base of 15 cm and a height of 8 cm, so the area of the triangle is A = (1/2) x 15 cm x 8 cm = 60 cm^2.
Now, we can find the volume of the triangular prism:
V_triangular_prism = 60 cm^2 x 8 cm = 480 cm^3
3. Total volume of the box:
To find the total volume, we add the volumes of the hexagonal prism and triangular prism:
Total volume = V_hexagonal_prism + V_triangular_prism
Total volume = 6232 cm^3 + 480 cm^3
Total volume = 6712 cm^3
Therefore, the volume of the box is 6712 cm^3.
thats not right
I apologize for the error. Let's correct the calculation:
1. Volume of the hexagonal prism:
The area of the hexagon base can be calculated using the formula for the area of a regular hexagon A = (3√3 x side length^2)/2.
Side length of the hexagon = 30 cm
A = (3√3 x 30^2)/2
A = (3√3 x 900)/2
A = (2700√3)/2
A = 1350√3 square cm
Volume of the hexagonal prism = base area x height
Volume = 1350√3 cm^2 x 8 cm = 10800√3 cubic cm (approximately 18707.8 cubic cm).
2. Volume of the triangular prism:
Base of the triangular prism is a right-angled triangle.
The area of the base triangle = (1/2) x base x height
Area = (1/2) x 15 cm x 8 cm = 60 square cm
Volume of the triangular prism = base area x height
Volume = 60 cm^2 x 8 cm = 480 cubic cm
3. Total volume of the box:
Total volume = Volume of hexagonal prism + Volume of triangular prism
Total volume = 10800√3 + 480
Total volume ≈ 18707.8 + 480
Total volume ≈ 19187.8 cubic cm
Therefore, the volume of the box is approximately 19187.8 cubic cm.
that also isnt right
I apologize for the errors. Let's correct the calculation:
1. Volume of the hexagonal prism:
The base area of the hexagon has been correctly calculated as 1350√3 square cm.
Now, to find the volume of the hexagonal prism:
Volume = base area x height
Volume = 1350√3 cm^2 x 8 cm
Volume = 10800√3 cubic cm
Volume ≈ 18720 cubic cm
2. Volume of the triangular prism:
The base area of the right-angled triangle has been correctly calculated as 60 square cm.
Now, to find the volume of the triangular prism:
Volume = base area x height
Volume = 60 cm^2 x 8 cm
Volume = 480 cubic cm
3. Total volume of the box:
Total volume = Volume of hexagonal prism + Volume of triangular prism
Total volume = 18720 cubic cm + 480 cubic cm
Total volume = 19184 cubic cm
Therefore, the volume of the box is 19184 cubic cm.