Answer to Question #149022 in Geometry for RV

Question

4. The lateral edge of a square prism is 20 cm long and it is inclined at an angle of 60 degrees with the base. If the volume of the prism is 1,200 cm3, determine the base edge.

5. The total area of a regular tetrahedron is 110.85 m2, determine its base edge.

6. If the lateral area of a right circular cylinder is 90 cm2 and its volume is 225 cm3, find its radius.

Answer 1

4. Volume of prism = B²h

B = base edge ; h = height

h = 20 sin(60$^{\circ}$ ) = 17.32cm

1200 = 17.32B²

=> B² = 69.28

=> B = $\sqrt{69.28}$ = 8.32cm

5. Area of tetrahedron = B²$\sqrt{3}$

110.85 = B²$\sqrt{3}$

=> B² = 64.00

B = $\sqrt{64.00}$

B = 8m

6. Volume of a cylinder = πr²h

Lateral area of cylinder = πrh

90 = π × r × h

=> h = $\frac{90}{πr}$

225 = πr²h

225 = $π×r²×\frac{90}{πr}$

225 = 90r

=> r = $\frac{225}{90} = 2.5cm$