Answer to Question #150159 in Geometry for 22

Question

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.

7. Determine the lateral area of a cylinder of height 300mm and base radius of 100mm.

Answer 1

5)Formula for total area of tetrahedron;

A=√3a² where a is the base edge

110.85=√3a²

Squaring both sides we have;

3a²=12287.72

Dividing both sides by 3 we have;

a²=4095.91

Taking the square root of both sides we have

a=64m

6)formula for lateral area of a right cylinder;

A=2πrh

Making h subject of the formula we have;

h=A/2πr

Formula for volume of the right cylinder is;

V=πr²h

Making h subject of the formula we have;

h=V/πr²

Equating the two heights we have;

A/2πr=V/πr²

After cancelling the like terms we have;

2V=Ar

V=225 and A=90 inserting our values we have;

450=90r

Dividing both sides by 90 we have;

r=5cm

7)lateral surface area of cylinder =2πrh

Converting the mm to cm we have

Height=30cm radius=10cm

Inserting our values we have

A=2xπ×30×10

A=600πcm² or 1885cm²