Question

Calculate the ratio of total surface area to the lateral surface area for the given figure below.

• A. $\frac{50}{71}$
• B. $\frac{71}{50}$
• C. $\frac{72}{50}$
• D. $\frac{71}{49}$

Answer 1

The correct option is B $\frac{71}{50}$

Given,

Length of the rectangular prism $=7$ unit

Breadth of the rectangular prism $=3$ unit

Height of the rectangular prism $=5$ unit

$\to$The lateral surface area of a rectangular prism= 2( l + b) h

$=2(7+3)\times 5$

$=100{\text{unit}}^2$

$\to$The total surface area of a rectangular prism $=2\left(lb\right)+2\left(bh\right)+2\left(lh\right)$

$=(2\times 7\times 3)+(2\times 3\times 5)+(2\times 5\times 7)=142{\text{unit}}^2$

Hence, The ratio is

$\frac{\text{Total surface area of a rectangular prism}}{\text{Lateral surface area of a rectangular prism}}=\frac{142}{100}=\frac{71}{50}$

Option (b) is correct.