Determine the surface area of the 3-dimensional figure 3 on the top 2 on the top 3 on the side 3 on the side 3 on the side 3 on the side 3 on the side 2 on the bottom
To find the surface area of this figure, we need to calculate the area of each of its faces and add them up.
- The top and bottom faces are both rectangles with dimensions 3 x 2, so the area of each is 6 square units. The total area of these two faces is 12 square units.
- The side faces are all rectangles with dimensions 3 x 3, so the area of each is 9 square units. There are four of these faces, so the total area of the side faces is 36 square units.
Adding up the areas of all the faces, we get:
12 + 36 = 48
Therefore, the surface area of the figure is 48 square units.
What is the volume of the figure?
3.2 on the side 10 on the bottom and 2.5 on the other side
To find the volume of this figure, we need to multiply its length, width, and height. Let's label the sides of the figure:
- Length: 3.2
- Width: 10
- Height: 2.5
Multiplying these three dimensions together, we get:
3.2 x 10 x 2.5 = 80
Therefore, the volume of the figure is 80 cubic units.
Two rectangular prisms, prism A and prism B, have the same height. The volume of prism A is half the volume of prism B. The base of prism A has an area of 40 square inches. What is the area of the base of prism B?
Let's assume that the height of both prisms is h, and let x be the area of the base of prism B. We already know that the area of the base of prism A is 40 square inches.
The volume of prism A is:
V(A) = 40h/2 = 20h
The volume of prism B is:
V(B) = xh
We know that the volume of prism A is half the volume of prism B, so we can set up an equation:
20h = xh/2
Simplifying this equation, we get:
40h = xh
Dividing both sides by h, we get:
x = 40
Therefore, the area of the base of prism B is 40 square inches.
A right rectangular prism has a height of 17.5 centimeters. The area of the base of the prism is 18 square centimeters. What is the volume, in cubic centimeters, of the right rectangular prism?
Let's assume that the length and width of the rectangular prism are L and W, respectively. We know that the height is 17.5 cm and the area of the base is 18 cm².
The volume of the rectangular prism is:
V = L x W x h
We know that the area of the base is:
A = L x W = 18
We can solve for one of the variables to get:
L = 18/W
Substituting this into the formula for the volume, we get:
V = (18/W) x W x 17.5
V = 315 cubic centimeters
Therefore, the volume of the right rectangular prism is 315 cubic centimeters.