Find the volume and total area of rectangular prism whose base is 5 inches x 9 inches x 12 inches.
Volume = length x width x height
= 5*9*12 cubic inches
= ..
surface area = area of the 6 faces of the prism
= 2(5*9) + 2(5*12) + 2(9*12) square inches
= ....
Why did the rectangular prism go to school? Because it wanted to learn how to calculate its volume and total area, of course! Well, let's be helpful and give this prism some knowledge.
To find the volume of a rectangular prism, you multiply the length, width, and height. So, for this prism with dimensions of 5 inches for length, 9 inches for width, and 12 inches for height, the volume would be 5 inches * 9 inches * 12 inches.
Now, let's grab our calculators! 5 times 9 is 45, and 45 times 12 is... drumroll, please... 540! So the volume of this rectangular prism is 540 cubic inches.
To find the total area, you need to calculate the area of each of the six faces and then add them up. The area of a rectangle is given by its length times its width.
The base consists of two rectangles with dimensions 5 inches by 9 inches. So the area of the base is 5 inches * 9 inches = 45 square inches.
The top also consists of two rectangles with the same dimensions, so the area of the top is also 45 square inches.
The sides are rectangles with dimensions of 5 inches by 12 inches, so the area of each side is 5 inches * 12 inches = 60 square inches. Since there are two sides, the total area of both sides is 2 * 60 = 120 square inches.
Finally, the front and back also have dimensions of 9 inches by 12 inches, so each has an area of 9 inches * 12 inches = 108 square inches. Since there are two fronts and two backs, the total area of the front and back combined is 2 * 108 = 216 square inches.
Now, let's add it all up. 45 (base) + 45 (top) + 120 (sides) + 216 (front and back) = 426 square inches.
So, the total area of this rectangular prism is 426 square inches. Voilà!
To find the volume of a rectangular prism, you need to multiply the length, width, and height together. In this case, the length is 9 inches, the width is 5 inches, and the height is 12 inches.
Volume = length x width x height
Volume = 9 inches x 5 inches x 12 inches
Volume = 540 cubic inches
So, the volume of the rectangular prism is 540 cubic inches.
To find the total surface area of a rectangular prism, you need to calculate the area of each face and add them together.
The rectangular prism has six faces: the top and bottom faces are both rectangles with dimensions 9 inches x 5 inches, the front and back faces are rectangles with dimensions 9 inches x 12 inches, and the left and right faces are rectangles with dimensions 5 inches x 12 inches.
We calculate the areas of each face and then sum them up:
Area of the top and bottom faces = length x width = 9 inches x 5 inches = 45 square inches each.
Area of the front and back faces = length x height = 9 inches x 12 inches = 108 square inches each.
Area of the left and right faces = width x height = 5 inches x 12 inches = 60 square inches each.
Total surface area = 2 x (Top and Bottom Area) + 2 x (Front and Back Area) + 2 x (Left and Right Area)
Total surface area = 2 x (45 square inches) + 2 x (108 square inches) + 2 x (60 square inches)
Total surface area = 90 square inches + 216 square inches + 120 square inches
Total surface area = 426 square inches.
So, the total surface area of the rectangular prism is 426 square inches.
To find the volume of a rectangular prism, you multiply the length, width, and height.
In this case, the base of the prism is given as 5 inches x 9 inches, and the height is 12 inches.
Volume = length x width x height
By substituting the values into the formula, we have:
Volume = 5 inches x 9 inches x 12 inches
To calculate this volume, we need to multiply the three values together:
Volume = 540 cubic inches
So, the volume of the rectangular prism is 540 cubic inches.
To find the total surface area of a rectangular prism, you add up the areas of all the faces.
For a rectangular prism, there are six faces: top, bottom, front, back, left, and right.
To find the area of a face, you multiply the length by the width.
In this case, the top and bottom faces have dimensions of 5 inches x 9 inches, the front and back faces have dimensions of 5 inches x 12 inches, and the left and right faces have dimensions of 9 inches x 12 inches.
So, the total surface area is calculated by adding the areas of all six faces:
Total Surface Area = 2(length x width) + 2(width x height) + 2(length x height)
Total Surface Area = 2(5 inches x 9 inches) + 2(5 inches x 12 inches) + 2(9 inches x 12 inches)
Simplifying this equation, we have:
Total Surface Area = 90 square inches + 120 square inches + 216 square inches
Total Surface Area = 426 square inches
So, the total surface area of the rectangular prism is 426 square inches.