Cube & Cuboid – Complete Solutions

 

Cube & Cuboid – Complete Solutions

1. The volume of a cube of side 8 cm is:

A) 256 cm³
B) 384 cm³
C) 512 cm³
D) 640 cm³

Solution:

Formula for volume of a cube:

$$\text{Volume} = a^3$$

Here, side $a = 8$ cm.

$$V = 8^3 = 8 \times 8 \times 8$$ $$V = 512\text{ cm}^3$$

✅ Correct Answer: C) 512 cm³

---

2. The total surface area of a cube of side 5 cm is:

A) 100 cm²
B) 125 cm²
C) 150 cm²
D) 180 cm²

Solution:

Formula for total surface area of a cube:

$$TSA = 6a^2$$

Here, $a = 5$ cm.

$$TSA = 6 \times 5^2$$ $$= 6 \times 25$$ $$= 150\text{ cm}^2$$

✅ Correct Answer: C) 150 cm²

---

3. The volume of a cuboid having dimensions 12 cm × 8 cm × 5 cm is:

A) 400 cm³
B) 420 cm³
C) 480 cm³
D) 500 cm³

Solution:

Formula for volume of a cuboid:

$$V = l \times b \times h$$

Given:

$$l=12\text{ cm},\quad b=8\text{ cm},\quad h=5\text{ cm}$$

Therefore,

$$V = 12 \times 8 \times 5$$ $$= 96 \times 5$$ $$= 480\text{ cm}^3$$

✅ Correct Answer: C) 480 cm³

---

4. If the side of a cube is doubled, its volume becomes:

A) 2 times
B) 4 times
C) 6 times
D) 8 times

Solution:

Volume of a cube is:

$$V=a^3$$

Let the original side be $a$.

Original volume:

$$V=a^3$$

When the side is doubled:

$$\text{New side}=2a$$

New volume:

$$V'=(2a)^3$$ $$V'=8a^3$$

Therefore,

$$V'=8V$$

So, the volume becomes 8 times the original volume.

✅ Correct Answer: D) 8 times

Exam Trick: If the side of a cube is multiplied by $n$, its volume becomes $n^3$ times.

---

5. A cube has a volume of 729 cm³. Its total surface area is:

A) 324 cm²
B) 486 cm²
C) 648 cm²
D) 729 cm²

Solution:

Volume of a cube:

$$V=a^3$$

Given:

$$a^3=729$$

We know:

$$9^3=729$$

Therefore,

$$a=9\text{ cm}$$

Now, total surface area:

$$TSA=6a^2$$ $$=6\times9^2$$ $$=6\times81$$ $$=486\text{ cm}^2$$

✅ Correct Answer: B) 486 cm²