A box of rice is shaped like a rectangular prism. The box has a length of 6 inches, a width of 1.5 inches, and a height of 8.5 inches.
What is the total surface area of the box in square inches?
A 136.5 in.2
B 76.5 in.2
C 145.5 in.2
D 127.5 in.2
The total surface area of a rectangular prism can be found by adding up the areas of all of its faces. We can use the formula:
surface area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height.
Substituting the given values, we get:
surface area = 2(6)(1.5) + 2(6)(8.5) + 2(1.5)(8.5)
surface area = 18 + 102 + 25.5
surface area = 145.5
Therefore, the total surface area of the box is 145.5 square inches, which is answer choice C.
Well, it seems like the rice box is really here to make our lives more interesting. Let's figure out the surface area, shall we?
To find the total surface area of the box, we need to calculate the area of all six sides and then add them up.
Starting with the front and back faces, which have the same dimensions as the length and height of the box, we can calculate their area as follows:
Front/Back Area = Length * Height = 6 in. * 8.5 in. = 51 in.²
Next, let's move on to the top and bottom faces, which have the same dimensions as the length and width of the box:
Top/Bottom Area = Length * Width = 6 in. * 1.5 in. = 9 in.²
Lastly, we'll calculate the area of the two remaining side faces, which have the same dimensions as the width and height:
Side Area = Width * Height = 1.5 in. * 8.5 in. = 12.75 in.²
Now, let's add up all these areas to find the total surface area of the rice box:
Total Surface Area = 2 * (Front/Back Area + Top/Bottom Area + Side Area)
= 2 * (51 in.² + 9 in.² + 12.75 in.²)
= 2 * (72.75 in.²)
= 145.5 in.²
So, the total surface area of the rice box is C) 145.5 in.². Now that's a well-rounded rice box!
To find the total surface area of the box, we need to calculate the area of each face and add them together.
The box has six faces: a top, bottom, front, back, left, and right.
1. Top and bottom face: These faces have the same dimensions and their area can be calculated by multiplying the length and width of the box.
Area of each top/bottom face = Length × Width = 6 in × 1.5 in = 9 in²
2. Front and back face: These faces have the same dimensions and their area can be calculated by multiplying the length and height of the box.
Area of each front/back face = Length × Height = 6 in × 8.5 in = 51 in²
3. Left and right face: These faces have the same dimensions and their area can be calculated by multiplying the width and height of the box.
Area of each left/right face = Width × Height = 1.5 in × 8.5 in = 12.75 in²
Now, we can calculate the total surface area by adding up the areas of all six faces.
Total surface area = 2 × (Area of top/bottom face) + 2 × (Area of front/back face) + 2 × (Area of left/right face)
= 2 × 9 in² + 2 × 51 in² + 2 × 12.75 in²
= 18 in² + 102 in² + 25.5 in²
= 145.5 in²
Therefore, the total surface area of the box is 145.5 in².
The correct answer is C) 145.5 in².
To calculate the total surface area of a rectangular prism, we need to find the area of each face and then add them up.
The rectangular prism has six faces: the top, bottom, front, back, left, and right faces.
1. The top and bottom faces are both rectangles with a length of 6 inches and a width of 1.5 inches. The formula for the area of a rectangle is length × width, so the area of each of these faces is 6 inches × 1.5 inches = 9 square inches.
2. The front and back faces are also rectangles with a length of 6 inches and a height of 8.5 inches. The area of each of these faces is 6 inches × 8.5 inches = 51 square inches.
3. The left and right faces are rectangles with a width of 1.5 inches and a height of 8.5 inches. The area of each of these faces is 1.5 inches × 8.5 inches = 12.75 square inches.
Now, we add up the areas of all six faces:
9 square inches (top) + 9 square inches (bottom) + 51 square inches (front) + 51 square inches (back) + 12.75 square inches (left) + 12.75 square inches (right) = 136.5 square inches.
Therefore, the total surface area of the box is 136.5 square inches, which corresponds to answer choice A.