Volume and surface area

Advanced Math 6 · Unit 12 · volume-surface-nets · Teacher edition

volume-surface-nets

Name ______________________________Date ______________

1.
A box measures $3$ cm by $4$ cm by $5$ cm. What is its surface area in cm²?
Answer: ______________
2.
Find the volume of a rectangular prism with edges $2\dfrac{1}{2}$ cm, $1\dfrac{1}{3}$ cm, and $3$ cm, in cm³.
Answer: ______________
3.
A cube has a surface area of $150$ cm². What is the length of one edge, in cm?
Answer: ______________
4.
A box measures $2 \times 3 \times 6$ . When its net is drawn, which of these is not the area of one of the faces?
1. (A)
  $6$
2. (B)
  $9$
3. (C)
  $12$
4. (D)
  $18$
5.
A rectangular tank has volume $7\dfrac{1}{2}$ cubic feet. Its base is $2\dfrac{1}{2}$ ft by $2$ ft. How tall is it, in feet?
Answer: ______________

Answer key — Volume and surface area

1.
94volume-surface-nets-01
$S = 2(12 + 15 + 20) = 2 \times 47 = \mathbf{94}$ cm². (Using $6 \times 3 \times 4 = 72$ treats it as a cube.)
2.
10volume-surface-nets-02
$\frac{5}{2} \times \frac{4}{3} \times 3 = \frac{5}{2} \times 4 = \mathbf{10}$ cm³.
3.
5volume-surface-nets-03
One face: $150 \div 6 = 25$ cm², so the edge is $\sqrt{25} = \mathbf{5}$ cm.
4.
(B)
$9$
volume-surface-nets-04
Faces: $6$ , $12$ , $18$ (each appearing twice). $\mathbf{9}$ is not a face area — it would need a $3 \times 3$ face, and there is no pair of equal edges.
5.
1.5volume-surface-nets-05
Base area $= \frac{5}{2} \times 2 = 5$ . Height $= \frac{15}{2} \div 5 = \frac{15}{10} = \mathbf{1\tfrac{1}{2}}$ ft. Check: $5 \times 1.5 = 7.5$ ✓.