Question

The edges of a cuboid are measured with a scale having an error of \(0.01\) cm per cm. If the dimensions of the cuboid are \[ (l,b,h)=(12,5,7), \] then the percentage error in the volume of the cuboid is

• A. \(1.79\)
• B. \(17.9\)
• C. \(3\)
• D. \(3.5\)

Hint:

For a product \[ V=lbh, \] the maximum relative error is \[ \boxed{ \frac{\Delta V}{V} = \frac{\Delta l}{l} + \frac{\Delta b}{b} + \frac{\Delta h}{h}. } \] Multiply the relative error by \(100\) to obtain the percentage error.

Answer 1

The Correct Option is C

Step 1: Write the formula for percentage error. The volume of a cuboid is \[ V=lbh. \] Hence, the maximum relative error is \[ \frac{\Delta V}{V} = \frac{\Delta l}{l} + \frac{\Delta b}{b} + \frac{\Delta h}{h}. \]

Step 2: Use the given measurement error. The scale has an error of \[ 0.01\text{ cm per cm}, \] which means each dimension has a relative error of \[ \frac{\Delta l}{l} = \frac{\Delta b}{b} = \frac{\Delta h}{h} = 0.01. \] Therefore, \[ \frac{\Delta V}{V} = 0.01+0.01+0.01 = 0.03. \]

Step 3: Find the percentage error. Thus, \[ \text{Percentage error} = 0.03\times100 = 3\%. \] Hence, \[ \boxed{3\%}. \] Thus, \[ \boxed{(C)} \] is the correct answer.