Question

A solid right prism made of iron has cross section of a triangle of sides 5cm, 10cm, 13cm and of height 10 cm. If one cubic cm of iron weights 7g, then the weight of the prism is (approximately)

Answer 1

Answer:  The answer is 1571.49 gm.

Step-by-step explanation: As given in the question and shown in the attached figure, ABCD is a solid right prism with triangular base BCD and height AQ = 10 cm. The weight of 1 cubic cm is 7 gm. We need to calculate the weight of the prism if sides of ΔBCD are 5 cm, 10 cm and 13 cm.

We know that

Area of prism ABCD = area of the base × height = area of ΔBCD × height.

First, we will calculate the area of ΔBCD.

We have

$s=\dfrac{5+10+13}{2}=14.$

So, area of ΔBCD will be

$b=\sqrt{s(s-5)(s-10)(s-13)}=\sqrt{14(14-5)(14-10)(14-13)}\\\\\Rightarrow b=6\sqrt{14}=22.45~\textup{cm}^2.$

Therefore, Volume of the prism = b × h = 22.45 × 10 = 224.5 cm³.

Now, weight of 1 cm³ = 7 gm.

Therefore, weight of 224.5 cm³ = 7 × 224.5 gm = 1571.49 gm.

Thus, the weight of the prism is 1571.49 gm.