Surface Area and Volume

Learn surface area, prism volume.

Lesson 3 of 32 parts Practice Flashcards

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Surface Area

Objective: Explain surface area, apply the stated method, and check its conditions.

A rectangular prism has three pairs of equal rectangular faces. Its surface area is 2(lw+lh+wh). This measures the total exterior area in square units, not the capacity of the solid; a net helps identify every face once. Count each face exactly once.

Formulas

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

Worked examples

Try itA rectangular prism is 6 cm by 7 cm by 7 cm. Find its surface area.Show answer

Step 1: Add the areas of the three pairs of faces. Step 2: Use 2(42+42+49). Step 3: Surface area is 266 cm².

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Surface Area

Objective: Explain surface area, apply the stated method, and check its conditions.

Formulas

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

Worked examples

Try itA rectangular prism is 6 cm by 7 cm by 7 cm. Find its surface area.Show answer

Step 1: Add the areas of the three pairs of faces. Step 2: Use 2(42+42+49). Step 3: Surface area is 266 cm².

Prism Volume

Objective: Explain prism volume, apply the stated method, and check its conditions.

A rectangular prism’s volume is lwh, equivalently base area times height. The dimensions must be measured in consistent length units. Volume counts three-dimensional space in cubic units and is distinct from the area covering the prism’s exterior. Volume is expressed in cubic units.

Formulas

$V=lwh$

Worked examples

Try itA rectangular prism is 6 cm by 7 cm by 7 cm. Find its volume.Show answer

Step 1: Volume counts cubic units filling the prism. Step 2: Use V=lwh=6·7·7. Step 3: V=294 cm³.

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