Find the way of the cast iron shape in the figure( Cast iron was 0.2607 lb/cu in. The base is an equilateral triangle with sides of 5,5 and a height of 6

Answer 1

To find the weight of the cast iron shape, we first need to find the volume of the shape.

The base of the shape is an equilateral triangle with side length 5 and height 6. The area of an equilateral triangle is given by the formula:
\[ A = \frac{√3}{4} \times \text{side length}^2 \]

Substitute the side length (5) into the formula:
\[ A = \frac{√3}{4} \times 5^2 = \frac{√3}{4} \times 25 = \frac{25√3}{4} \]

Next, the volume of the shape can be calculated by multiplying the area of the base by the height:
\[ V = A \times \text{height} = \frac{25√3}{4} \times 6 = \frac{150√3}{4} \]

Since the density of cast iron is 0.2607 lb/cu in, we can now calculate the weight of the cast iron shape:
\[ \text{Weight} = \text{Volume} \times \text{Density} = \frac{150√3}{4} \times 0.2607 ≈ 19.6274 \text{ lb} \]

Therefore, the weight of the cast iron shape is approximately 19.63 lbs.