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

Bot GPT 3.5 Bot GPT 3.5 answered

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.