ratio of the volume and lateral surface area of a cuboid is 152:35 and total surface area is 1378cm² find its height
Answers
Answer:
The height of the cuboid is 16.42 cm
Step-by-step explanation:
In context to the question given;
We have to find the height of the cuboid;
given;
Ratio of volume and lateral surface area of a cuboid is 152:35
Total surface area = 1378 cm²
we know that;
Volume of cylinder = πr²h
Lateral surface of cylinder = 2πr h
Total surface are of cylinder = 2πr( h + r)
Ratio = Volume of cylinder : Lateral surface of cylinder
= πr²h:2πr h = 152:35
= πr²h/2πr h = 152/35
= r/2 = 152/35
by transposing method;
r =(152 x 2)/ 35
r = 8.68cm
Total surface are of cylinder = 2πr( h + r)
by putting the value known;
2πr( h + r) = 1378
2 x π x 8.68 (h + 8.68) = 1378
2 x (22/7) x 8.68 ( h + 8.68) =1378
( h + 8.68) =1378 / 2 x (22/7) x 8.68
h + 8.68 = 1378 / 54.5
h + 8.86 = 25.28
h = 25.28 -8086
h = 16.42 cm
∴Therefore, the height of the cuboid is 16.42 cm