Question

A hallow cylindrical rod is planned to
manufacture with radius equals to the area
1613 cm2 of equilateral triangle and the height
equals the perimeter of that triangle. Then
what will be the rod's holding capacity ?

Answer 1

Given :

The radius of hallow cylinder = each side of equilateral triangle

The height of hallow cylinder = Perimeter of equilateral triangle

The  Area of equilateral triangle = 1613 sq cm

To Find :

The cylinder rod capacity

Solution :

∵  Area of equilateral triangle = $\dfrac{\sqrt{3} }{4}$ × side²

Or,  1613 sq cm = $\dfrac{\sqrt{3} }{4}$ × a²

Or,   1613 sq cm = 0.433 × a²

∴   a² = $\dfrac{1613}{0.433}$

         = 3725

i.e Measure of side = a = 61 cm

So, radius of hallow cylinder = a = 61 cm

Again

Perimeter of equilateral triangle = 3 × side

                                                      = 3 × 61 cm

                                                      = 183 cm

So, Height of hallow cylinder =  Perimeter of equilateral triangle = 183 cm

Now,

capacity of cylinder rod = Volume of hallow cylinder = π × radius² × height

i.e Volume of hallow cylinder = 3.14 × (61 cm)² × 183 cm

                                                 = 3.14 × 3721 cm² × 183 cm

                                                  = 2138161.02 cm³

Hence, The capacity of cylinder rod is 213861.02 cubic cm   Answer