Surface Area of a Cuboid: Express using

To find the surface area of the rectangular prism in terms of $X$, follow these steps:

• Step 1: Identify the dimensions:
  • Length $l = X$
  • Width $w = 5$
  • Height $h = 3$
• Step 2: Use the surface area formula for a rectangular prism: $S = 2(lw + lh + wh)$
• Step 3: Substitute the given values: $S = 2(X \cdot 5 + X \cdot 3 + 5 \cdot 3)$
• Step 4: Simplify the expression: $S = 2(5X + 3X + 15)$ $S = 2(8X + 15)$ $S = 16X + 30$
• Step 5: Therefore, the surface area of the rectangular prism expressed in terms of $X$ is $16X + 30$.

This matches with choice 1.

Thus, the solution to the problem is $16X + 30$.

The problem requires us to find the surface area of a rectangular prism in terms of $a$, $b$, and $c$. To find this, we use the standard formula for the surface area of a cuboid.

The surface area of a cuboid is given by:

$S = 2(ab + bc + ca)$

Explanation of the formula:

• Each face of the cuboid is a rectangle. There are three unique rectangles in a cuboid:
• Two faces with dimensions $a \times b$,
• Two faces with dimensions $b \times c$,
• Two faces with dimensions $c \times a$.

These three pairs of faces contribute to the total surface area as follows:

• Area of the two $a \times b$ faces: $2 \times (ab)$
• Area of the two $b \times c$ faces: $2 \times (bc)$
• Area of the two $c \times a$ faces: $2 \times (ca)$

Adding these areas together gives us the total surface area:

$S = 2ab + 2bc + 2ca$

This simplifies to $2(ab + bc + ca)$.

Given the choices, the correct expression for the surface area is $2ac + 2ab + 2bc$.

To solve this problem, we'll recall the following relevant formula:

• The surface area of a cube is given by the formula: $\text{Surface Area} = 6a^2$.

Let's break down the solution in steps:

Step 1: Identify the characteristic of the cube.
A cube is a three-dimensional shape with six identical square faces.

Step 2: Determine the area of one face.
Each face of the cube is a square with side length $a$, so the area of one face is $a^2$.

Step 3: Calculate the total surface area.
Since a cube has six identical faces, the total surface area is six times the area of one face:

$\text{Surface Area} = 6 \times a^2 = 6a^2$

Therefore, the surface area of the cube in terms of $a$ is $6a^2$.

To solve this problem, we must find the surface area of the rectangular prism with given dimensions $1$, $5$, and $a$.

The formula for the surface area $S$ of a rectangular prism with length $l$, width $w$, and height $h$ is:

$S = 2(lw + lh + wh)$

For this prism, let's identify the dimensions:

• Length ($l$) = 1
• Width ($w$) = 5
• Height ($h$) = a

Now, substitute these dimensions into the surface area formula:

$S = 2(1 \times 5 + 1 \times a + 5 \times a)$

Simplify the expression inside the parentheses:

$S = 2(5 + a + 5a)$

Combine the terms:

$S = 2(5 + 6a)$

Multiply through by 2:

$S = 10 + 12a$

Thus, the surface area of the rectangular prism expressed in terms of $a$ is $12a + 10$.

To find the surface area of a cuboid, I need to identify its three dimensions from the diagram and apply the surface area formula.

From the SVG diagram labels, the three dimensions of the cuboid are:

• Length: $a^2$
• Width: $a + 2$
• Height: $a$

The surface area formula for a cuboid with dimensions $l$, $w$, and $h$ is:
$SA = 2(lw + lh + wh)$

Let me calculate each face area:

• Face 1 (length × width): $a^2 \cdot (a+2) = a^3 + 2a^2$
• Face 2 (length × height): $a^2 \cdot a = a^3$
• Face 3 (width × height): $(a+2) \cdot a = a^2 + 2a$

Now, applying the surface area formula:
$SA = 2[(a^3 + 2a^2) + a^3 + (a^2 + 2a)]$
$SA = 2[2a^3 + 3a^2 + 2a]$
$SA = 4a^3 + 6a^2 + 4a$

Therefore, the surface area of the cuboid expressed in terms of $a$ is $4a^3 + 6a^2 + 4a$.

To find the surface area of a cuboid, we consider its six rectangular faces. A cuboid has three pairs of opposite faces. Each pair of faces shares the same area.

The surface area $S$ of a cuboid with dimensions $a$, $b$, and $c$ is calculated by finding the area of each of these rectangular faces and then summing them up. Specifically, we consider:

• The area of the first pair of opposite faces with dimensions $a$ and $b$ is $ab$.
• The area of the second pair of faces with dimensions $b$ and $c$ is $bc$.
• The area of the third pair of faces with dimensions $a$ and $c$ is $ac$.

The total surface area is thus given by the formula:

$S = 2(ab + bc + ac)$

By analyzing the provided choices, it's clear that the correct formula for the surface area of the cuboid is $2(a\times b + b\times c + a\times c)$.

Therefore, the solution to the problem is $2(a \times b + b \times c + a \times c)$.