Question

A wooden ramp in the shape of a right triangular prism with base, height and length as $6$ cm, $8$ cm and $13$ cm respectively is to be constructed. If the price of wood is
$\$2.5/c{m}^2$, how much (in dollars) will it cost to build the ramp?

• A. $\$600$
• B. $\$900$
• C. $\$1000$
• D. None of the above

Answer 1

The correct option is B $\$900$


To calculate the amount of wood required to build this ramp, we have to calculate the total surface area.

Total Surface Area = Lateral Surface Area $+$ Area of two triangluar sides

Lateral Surface Area:
From Pythagoras theorem,
Hypotaneus of the triangluar sides
$=\sqrt[2]{2h^2+b^2}$, where $h$ and $b$ are the height and base of the triangle respectively.

$⟹\text{Hypotaneus}=\sqrt[2]{28^2+6^2}=\sqrt[2]{264+36}=\sqrt[2]{2100}=10cm$

$\therefore$ Lateral Surface Area of the prism $=(l+b+h)\times$ length of the prism

$=(8+6+10)\times 13$

$=24\times 13=312$ cm

Surface Area for the triangular parts:
$\text{Height = h = 8 cm}$
$\text{Base = b = 6 cm}$

$\therefore \text{Area of a rectangle}=\frac{1}{2}\times h\times b$

$=\frac{1}{2}\times 8\times 6$

$=\frac{1}{2}\times 48=24c{m}^2$

And, area of the two triangular sides $=24+24=48$ cm${}^2$

Thus total surface area $=$ Lateral Surface Area $+$ Area of two triangluar sides $=312+48=360$ cm${}^2$, which is also the amount of wood required for construction.

With the rate being $\$2.5/c{m}^2$,
Cost of building this ramp will be $=360\times 2.5=\$900$

Option (b.) is correct.