Answer to Question #148567 in Geometry for marshy taray

Question

A square prism that has 5m base, 6m height,and 7 m width.
The lateral edge of a square prism is 30 cm long and it is inclined at an angle of 70 degrees with the base. If the volume of the prism is1,500cm3,
1.what is the base edge?
2.What is the capacity of the trough in m3?
3.What is the wetted surface area of the trough if it is fully filled with water?

Answer 1

$\text{1. Length(L)}=30{cm} \text{; Volume (V) = }1500cm^3\\\text{V=Area of base}\cdot\text{height} \\ \implies 1500cm^3=\text{ Area of base}\cdot30cm\\ \text{Dividing both sides by 30cm we have: Area of base = }\frac{1500cm^3}{30}=50cm^2\\ \text{Since it is a square prism, then the base edge = }\sqrt{50cm^2}=7.071cm\\ \text{2. We know that }1m^3=10^6 cm^3 \implies 1500cm^3=\frac{1500}{10^6}m^3=1.5*10^{-3}m^3\\ \text{3. Suface area = lateral area + base area }= 4ah + a^2\\ \text{Where a is the base edge and h is the height of the trough }\\ \implies \text{Surface area }= 4*7.071*30 + 50=898.52cm^2$