Question

abbreviations
surface area

• sa = surface area
• l = length
• w = width
• h or h = height
• s = side
• r = radius
• $sa = 2lw + 2lh+2wh$ (surface area of a rectangular solid)
• $sa = 6s^{2}$ (surface area of a cube)
• $sa = 4pi r^{2}$ (surface area of a sphere)
• $sa = 2pi rh+2pi r^{2}$ (surface area of a right circular cylinder)

abbreviations
volume

• v = volume
• l = length
• w = width
• h or h = height
• s = side
• r = radius
• $v = lwh$ (volume of a rectangular solid)
• $v = s^{3}$ (volume of a cube)
• $v=\frac{4}{3}pi r^{3}$ (volume of a sphere)
• $v=pi hr^{2}$ (volume of a right circular cylinder)

find the surface area in square meters and volume in cubic centimeters of the figure below.

image of a rectangular - solid with dimensions 15 m, 6 m, 13 m
surface area =
square meters
volume =
cubic centimeters
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Explanation:

Step1: Identify the formula for surface area of rectangular solid

The formula for the surface area of a rectangular solid is $SA = 2LW+2LH + 2WH$, where $L = 15$ m, $W=6$ m, and $H = 13$ m.

Step2: Calculate the surface area

\[

$$\begin{align*} SA&=2\times15\times6+2\times15\times13+2\times6\times13\\ &=180 + 390+156\\ &=726 \end{align*}$$

\]
So the surface - area is 726 square meters.

Step3: Identify the formula for volume of rectangular solid

The formula for the volume of a rectangular solid is $V = LWH$, where $L = 15$ m, $W = 6$ m, and $H=13$ m. First, calculate the volume in cubic meters: $V=15\times6\times13=1170$ m³.

Step4: Convert volume from cubic meters to cubic centimeters

Since 1 m³ = 1000000 cm³, then $V=1170\times1000000 = 1170000000$ cm³.

Answer:

Surface Area = 726 square meters
Volume = 1170000000 cubic centimeters