Question

find the weight of the cast iron shape in the figure. (cast iron weighs 0.2607 lb/cu in. the base is an equilateral triangle.) the weight of the cast iron shape is __ lb. (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate base area of equilateral - triangle

The area formula for an equilateral triangle with side length $s$ is $A=\frac{\sqrt{3}}{4}s^{2}$. Here, $s = 5$ inches, so $A=\frac{\sqrt{3}}{4}\times5^{2}=\frac{25\sqrt{3}}{4}\text{ in}^2$.

Step2: Calculate volume of the prism

The volume formula for a prism is $V=A\times h$, where $A$ is the base - area and $h$ is the height. Here, $h = 8$ inches. So $V=\frac{25\sqrt{3}}{4}\times8=50\sqrt{3}\text{ in}^3$.

Step3: Calculate the weight

The weight formula is $W=\text{density}\times V$. The density of cast - iron is $0.2607$ lb/cu in. So $W = 0.2607\times50\sqrt{3}\approx0.2607\times50\times1.732 = 0.2607\times86.6\approx22.6$ lb.

Answer:

$22.6$