Question

Imagine a picture of a scoop of ice-cream in a cone. Consider the cone to be in equilateral shape and the scoop to fit at the top of the cone. What would be the area of the picture if the side of the equilateral triangle is, a = 6 cm?

• A. 25.31 cm²
• B. 32.45 cm²
• C. 29.71 cm²
• D. 27.98 cm²

Answer 1

The correct option is C

29.71 cm²

Here for finding the area of the picture, we can simplify the diagram

into a equilateral cone and a semicircle above the triangle. We already

know that the side of the equilateral triangle is a = 6 cm.

We also know that the area of an equilateral triangle is = $\frac{\sqrt{3}}{4}\times a^2$

= $\frac{\sqrt{3}}{4}\times 6^2$

= $\frac{\sqrt{3}}{4}\times 36$

= $9\sqrt{3}c{m}^2$

Now let us consider the semi-circular part, we know from the

diagram that the side of the triangle is equal to the diameter of the semicircle, i.e. d = a =6 cm.

Therefore the area of the semicircle will be =$\frac{1}{2}\times \pi \times (\frac{d}{2}{)}^2$

= $\frac{1}{2}\times \frac{22}{7}\times (\frac{6}{2}{)}^2$

= $\frac{11}{7}\times 3^2$

= $\frac{99}{7}$

= 14.14 $c{m}^2$

So, the area of the picture = area of the triangle + Area of the semi-circle

= $9\sqrt{3}$ + 14.14

= 9 x 1.73 + 14.14

= 15.57 + 14.14

= 29.71 $c{m}^2$

The area of the picture of ice cream is 29.71 $c{m}^2$