Volume and Surface Area of 3D Shapes worksheet - Free Printable

Here are the step-by-step solutions for each shape on your worksheet.

Row 1

1. Rectangular Prism (Box)
* Dimensions: Length = 10 mm, Width = 6 mm, Height = 3 mm
* Volume: Multiply length × width × height.
$$10 \times 6 \times 3 = 180$$
* Surface Area: Add the area of all 6 sides (Top/Bottom, Front/Back, Left/Right).
* Top/Bottom: $10 \times 6 = 60$ (two of these is 120)
* Front/Back: $10 \times 3 = 30$ (two of these is 60)
* Left/Right: $6 \times 3 = 18$ (two of these is 36)
* Total: $120 + 60 + 36 = 216$

2. Cube
* Dimensions: Side = 4 mm
* Volume: Side × Side × Side.
$$4 \times 4 \times 4 = 64$$
* Surface Area: A cube has 6 identical square faces.
* Area of one face: $4 \times 4 = 16$
* Total: $16 \times 6 = 96$

3. Cylinder
* Dimensions: Radius ($r$) = 7 cm, Height ($h$) = 10 cm
* Volume: $\pi \times r^2 \times h$. (Using $\pi \approx 3.14$)
* $3.14 \times 7^2 \times 10$
* $3.14 \times 49 \times 10$
* $153.86 \times 10 = 1538.6$
* Surface Area: $2\pi r^2 + 2\pi rh$ (Two circles + the side rectangle).
* Circles: $2 \times 3.14 \times 49 = 307.72$
* Side: $2 \times 3.14 \times 7 \times 10 = 439.6$
* Total: $307.72 + 439.6 = 747.32$

4. Triangular Prism
* Dimensions: Triangle Base = 15 cm, Triangle Height = 8 cm, Prism Length = 10 cm. The slanted side is 17 cm.
* Volume: Area of triangle base × Prism Length.
* Triangle Area: $\frac{1}{2} \times 15 \times 8 = 60$
* Volume: $60 \times 10 = 600$
* Surface Area: Two triangles + Three rectangles.
* Two Triangles: $60 \times 2 = 120$
* Bottom Rectangle: $15 \times 10 = 150$
* Back Rectangle: $8 \times 10 = 80$
* Slanted Rectangle: $17 \times 10 = 170$
* Total: $120 + 150 + 80 + 170 = 520$

---

Row 2

5. Square Pyramid
* Dimensions: Base side = 4 yd, Slant height = 10 yd.
* Surface Area: Base Area + Area of 4 triangular faces.
* Base: $4 \times 4 = 16$
* One Triangle: $\frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 4 \times 10 = 20$
* Four Triangles: $20 \times 4 = 80$
* Total: $16 + 80 = 96$
*(Note: We cannot calculate volume because the vertical height inside the pyramid is not given).*

6. Rectangular Pyramid
* Dimensions: Base = 8 cm by 3 cm, Vertical Height ($h$) = 10 cm.
* Volume: $\frac{1}{3} \times \text{Base Area} \times \text{Height}$.
* Base Area: $8 \times 3 = 24$
* Volume: $\frac{1}{3} \times 24 \times 10$
* $8 \times 10 = 80$

7. Triangular Prism
* Dimensions: Triangle Base = 8 m, Triangle Height = 3 m, Prism Length = 6 m. The slanted side is 5 m.
* Volume: Area of triangle base × Prism Length.
* Triangle Area: $\frac{1}{2} \times 8 \times 3 = 12$
* Volume: $12 \times 6 = 72$
* Surface Area: Two triangles + Three rectangles.
* Two Triangles: $12 \times 2 = 24$
* Bottom Rectangle: $8 \times 6 = 48$
* Back Rectangle: $3 \times 6 = 18$
* Slanted Rectangle: $5 \times 6 = 30$
* Total: $24 + 48 + 18 + 30 = 120$

8. Cylinder
* Dimensions: Diameter = 10 cm (so Radius is 5 cm), Height = 8 cm.
* Volume: $\pi \times r^2 \times h$.
* $3.14 \times 5^2 \times 8$
* $3.14 \times 25 \times 8$
* $78.5 \times 8 = 628$
* Surface Area: $2\pi r^2 + 2\pi rh$.
* Circles: $2 \times 3.14 \times 25 = 157$
* Side: $2 \times 3.14 \times 5 \times 8 = 251.2$
* Total: $157 + 251.2 = 408.2$

──────────────────────────────────────

Final Answer:

Row 1:
1. Rectangular Prism: Volume = 180 mm³, Surface Area = 216 mm²
2. Cube: Volume = 64 mm³, Surface Area = 96 mm²
3. Cylinder: Volume = 1538.6 mm³ (or cm³ depending on label typo), Surface Area = 747.32 mm²
4. Triangular Prism: Volume = 600 cm³, Surface Area = 520 cm²

Row 2:
5. Square Pyramid: Surface Area = 96 yd²
6. Rectangular Pyramid: Volume = 80 cm³
7. Triangular Prism: Volume = 72 m³, Surface Area = 120 m²
8. Cylinder: Volume = 628 cm³, Surface Area = 408.2 cm²