Answer to Question #148569 in Geometry for marshy taray

Question

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 is 1,500 cm, The base of the right prism is an equilateral triangle. The area of the base
is 1,560 cm? If the altitude of the prism is 5 meters,
What is the base edge of the prism in cm?
What is the lateral area of the prism in m?
What is the volume of the prism in m?

Answer 1

Lateral edge,d = 30cm or 0.3m

Volume,V = 1500cm³ or 0.0015m³

a) Volume = B²d

d = 30 * sin(70^o) = 28.2cm

B² = V/d

B² = V/d

B² = 1500/28.2

B² = 53.19

B = 7.29cm²

b) Lateral area of the prism, A_L = 4Bd

A_L = 4 * 7.3 * 28.2

A_L = 823.44cm² or 0.082344m²

c) Volume as stated in the question is 1500cm³ or 0.0015m³