Question

A cylindrical water tank has radius $7\text{ m}$ and height $10\text{ m}$. What is its volume?}

• A. $1540\text{ m}^3$
• B. $490\text{ m}^3$
• C. $980\text{ m}^3$
• D. $3080\text{ m}^3$

Hint:

Whenever a cylinder or circle problem gives a radius that is a multiple of 7 (7, 14, 21...) with $\pi=\frac{22}{7}$, work out the base area first -- it always comes out as a whole number -- then just multiply by the height. This avoids messy fraction cancellation in the full formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The volume of a cylinder represents the total space occupied by the object. Since the base of a cylinder is a circle, the volume is calculated by multiplying the area of the circular base by the height of the cylinder.

Step 2: Identifying the Formula and Values:
The formula for the volume ($V$) of a cylinder is: \[ V = \pi r^2 h \] Given values:
• Radius ($r$) = $7\text{ m}$
• Height ($h$) = $10\text{ m}$
• $\pi \approx \frac{22}{7}$

Step 3: Calculation:
Substitute the values into the formula: \[ V = \frac{22}{7} \times (7)^2 \times 10 \] \[ V = \frac{22}{7} \times 49 \times 10 \] Cancel the common factor of $7$: \[ V = 22 \times 7 \times 10 \] \[ V = 154 \times 10 = 1540\text{ m}^3 \]

Step 4: Final Answer:
The volume of the water tank is $1540\text{ m}^3$.

Answer 2

Concept:

• When the radius is a multiple of 7 and $\pi$ is taken as $\frac{22}{7}$, the base circle area always comes out as a clean whole number -- compute it first, then just multiply by the height.

Step 1: Compute the base area using the radius-7 shortcut.
Whenever the radius is a multiple of 7 and $\pi = \frac{22}{7}$ is used, the 7 in the radius cancels the 7 in the denominator, giving a clean whole number directly:
$\text{Base Area} = \pi r^2 = \frac{22}{7} \times 7 \times 7 = 22 \times 7 = 154\text{ m}^2$

Step 2: Use volume = base area x height directly.
There is no need to substitute $r$ and $h$ into the full formula $V=\pi r^2 h$ and simplify fractions each time -- once the base area is known, the volume is simply that area multiplied by the height.

Step 3: Multiply by the height.
$V = \text{Base Area} \times h = 154 \times 10 = 1540\text{ m}^3$

Final Answer: The volume of the water tank is $1540\text{ m}^3$.