Question

question of the week
question 1
an open - topped paper drinking cup in the shape of a cone is pictured below.
which is closest to the amount of paper required to make the cup?
a 185 cm²
b 167 cm²
c 135 cm²
d 126 cm²
solution video

Explanation:

Step1: Find the radius

The diameter of the cone is \(d = 8\mathrm{cm}\), so the radius \(r=\frac{d}{2}=\frac{8}{2}=4\mathrm{cm}\).

Step2: Find the slant height \(l\)

Using the Pythagorean theorem \(l=\sqrt{r^{2}+h^{2}}\), where \(h = 10\mathrm{cm}\) and \(r = 4\mathrm{cm}\). Then \(l=\sqrt{4^{2}+10^{2}}=\sqrt{16 + 100}=\sqrt{116}\approx10.77\mathrm{cm}\).

Step3: Calculate the lateral - surface area of the cone

The formula for the lateral - surface area of a cone is \(A=\pi rl\). Substitute \(r = 4\mathrm{cm}\) and \(l\approx10.77\mathrm{cm}\) into the formula: \(A=\pi\times4\times10.77\). Using \(\pi\approx3.14\), we get \(A\approx3.14\times4\times10.77=3.14\times43.08 = 135.2712\mathrm{cm}^{2}\).

Answer:

c. \(135\mathrm{cm}^{2}\)