Question

Imagine a picture of a scoop of ice-cream in a cone. Draw a picture, considering the cone to be in the shape of an equilateral triangle and the scoop, to be in the shape of a semi circle, to fit exactly on the side of the equilateral triangle. What is the area of the picture if the side of the equilateral triangle is, a = 6 cm?

• A. 30.71 $c{m}^2$
• B. 29.71 $c{m}^2$
• C. 26 $c{m}^2$
• D. 39 $c{m}^2$

Answer 1

The correct option is B

29.71 $c{m}^2$

Here for finding the area of the picture, we can simplify the diagram into a equilateral cone and a semicircle above the triangle.

Side of the equilateral triangle is a = 6 cm.

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 =$\frac{1}{2}\times \pi \times (\frac{d}{2}{)}^2$

= $\frac{1}{2}\times 3.14\times (\frac{6}{2}{)}^2$

= 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 $c{m}^2$