Question

A manufacturer designs a BBQ from an old steel drum with a diameter of 55 cm. As shown a section 25 cm wide is cut off the top of the drum to enable a grilling surface. He wants to advertise the depth of the BBQ so it can double as a smoker. How deep will the BBQ be? (adapted from Big Ideas from Dr. Small Grade 9-12)

Answer 1

Solution

The length of the chord = 25cm

The diameter = 55cm

The radius = 55/2 = 27.5cm

Using pythagoras theorem

$Hyp^2=opp^2+adj^2$

Hypotenuse = 27.5cm

Opposite = h

Adjacent = 12.5cm

$\begin{gathered} 27.5^2=12.5^2+x^2 \\ 756.25=156.25+x^2 \\ 756.25-156.25=x^2 \\ 600=x^2 \\ x=\sqrt{600} \\ x=24.49cm \end{gathered}$

Therefore the depth of the BBQ = 24.49cm