Question #150725
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.
1
Expert's answer
2020-12-15T02:16:44-0500

5).

A = 3\sqrt3 a2

a2 = A3\frac{A}{\sqrt3}


a2 = 110.853\frac{110.85}{\sqrt3}


a = 7.99995m

a = 8m


6).

Area of right circular cylinder is A=2πrhA= 2\pi r h and volume is V=πr2hV= \pi r^2 h . Thus we have

2πrh=90rh=45π......Eq[1]r2h=225π.......Eq[2]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=22545r=5cm.....Ansr=\cfrac{225}{45}\\ r= 5cm.....Ans

radius of right circular cylinder is 5 cm.


7).

h=300  mmr=100  mmLateral  area  of  cylinder=2πrh=2×3.14×100×300=188520  mm2h = 300\; mm \\ r = 100 \;mm \\ Lateral \;area\; of \;cylinder = 2πrh \\ = 2 \times 3.14 \times 100 \times 300 \\ = 188520 \; mm^2

Answer: 188520 mm2

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