Answer to Question #150725 in Geometry for Janvi Lazaro

Question

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).

A = $\sqrt3$ a²

a² = $\frac{A}{\sqrt3}$

a² = $\frac{110.85}{\sqrt3}$

a = 7.99995m

a = 8m

6).

Area of right circular cylinder is $A= 2\pi r h$ and volume is $V= \pi r^2 h$ . Thus we have

$$2\pi rh= 90 \\ rh =\cfrac{45}{\pi}......Eq[1]\\ r^2 h=\cfrac{225}{\pi}.......Eq[2]$$

Now dividing Eq[2] by Eq[1]...

$$r=\cfrac{225}{45}\\ r= 5cm.....Ans$$

radius of right circular cylinder is 5 cm.

7).

$h = 300\; mm \\ r = 100 \;mm \\ Lateral \;area\; of \;cylinder = 2πrh \\ = 2 \times 3.14 \times 100 \times 300 \\ = 188520 \; mm^2$

Answer: 188520 mm²