Testinar Grade 7 math

Surface Area of Three-Dimensional Objects

Students will build Grade 7 mastery of surface area of three-dimensional objects using models, equations, and test-style reasoning.

CH07-05 Measurement Geometry

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A rectangular prism has length \(4\) cm, width \(3\) cm, and height \(5\) cm. What is its surface area?
1. \(47\) cm\(^2\)
2. \(60\) cm\(^2\)
3. \(94\) cm\(^2\)
4. \(120\) cm\(^2\)
A cube has edge length \(6\) cm. Find its surface area.
1. \(36\) cm\(^2\)
2. \(72\) cm\(^2\)
3. \(144\) cm\(^2\)
4. \(216\) cm\(^2\)
A rectangular prism with dimensions \(5\) m \(\times\) \(3\) m \(\times\) \(2\) m is shown above. Calculate its surface area.
1. \(30\) m\(^2\)
2. \(62\) m\(^2\)
3. \(84\) m\(^2\)
4. \(120\) m\(^2\)
A rectangular prism has length \(7\) cm, width \(2\) cm, and height \(4\) cm. What is the total surface area?
1. \(56\) cm\(^2\)
2. \(72\) cm\(^2\)
3. \(100\) cm\(^2\)
4. \(112\) cm\(^2\)
A cube has surface area \(150\) cm\(^2\). What is the edge length of the cube?
1. \(5\) cm
2. \(6\) cm
3. \(25\) cm
4. \(30\) cm
The rectangular prism shown has dimensions \(3\) in \(\times\) \(2\) in \(\times\) \(4\) in. What is its surface area?
1. \(32\) in\(^2\)
2. \(52\) in\(^2\)
3. \(64\) in\(^2\)
4. \(96\) in\(^2\)
A cube has edge length \(4\) cm. What is the total surface area?
1. \(16\) cm\(^2\)
2. \(64\) cm\(^2\)
3. \(96\) cm\(^2\)
4. \(128\) cm\(^2\)
A rectangular prism has dimensions \(6\) cm \(\times\) \(4\) cm \(\times\) \(3\) cm. What is its surface area?
1. \(72\) cm\(^2\)
2. \(108\) cm\(^2\)
3. \(144\) cm\(^2\)
4. \(216\) cm\(^2\)

Teacher and parent reference

Answer key and explanations

C. \(94\) cm\(^2\)
\(SA=2(lw+lh+wh)=2(4\cdot3+4\cdot5+3\cdot5)=2(12+20+15)=2(47)=94\) cm\(^2\).
D. \(216\) cm\(^2\)
A cube has 6 faces, each a square with side length \(6\) cm. \(SA = 6s^2 = 6(6)^2 = 6(36) = 216\) cm\(^2\).
B. \(62\) m\(^2\)
\(SA = 2(5 \cdot 3 + 5 \cdot 2 + 3 \cdot 2) = 2(15 + 10 + 6) = 2(31) = 62\) m\(^2\).
C. \(100\) cm\(^2\)
\(SA = 2(lw + lh + wh) = 2(7 \cdot 2 + 7 \cdot 4 + 2 \cdot 4) = 2(14 + 28 + 8) = 2(50) = 100\) cm\(^2\).
A. \(5\) cm
If \(SA = 6s^2 = 150\), then \(s^2 = 25\), so \(s = 5\) cm.
B. \(52\) in\(^2\)
\(SA = 2(3 \cdot 2 + 3 \cdot 4 + 2 \cdot 4) = 2(6 + 12 + 8) = 2(26) = 52\) in\(^2\).
C. \(96\) cm\(^2\)
\(SA = 6s^2 = 6(4)^2 = 6(16) = 96\) cm\(^2\).
B. \(108\) cm\(^2\)
\(SA = 2(6 \cdot 4 + 6 \cdot 3 + 4 \cdot 3) = 2(24 + 18 + 12) = 2(54) = 108\) cm\(^2\).