The length, breath and height of a box are in the ratio 5:4:3 and the length of it’s diagonal is root 10 m, Find the total surface area.
Answers
Step-by-step explanation:
1
The length, breadth, and height of a cuboid are in ratio 5:4:2. If it's total surface area is 1216 cm square, what is the volume of the solid?
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Brian Baker
Answered February 7, 2018
Kind of a fun question because you’re starting with area which is a square and then converting a to a cubic. Surface area of a cuboid is basically 2 of each rectangle created by the measurements sides. The sides are created by taking the missing factor (x) in the 5:4:2 proportion, solve for x and you have the lengths and then the volume is easy.
2(2x*4x + 2x*5x + 4x*5x) = 1216 cm^2
8x^2 + 10x^2 + 20x^2 = 608 cm^2
38x^2 = 608 cm^2
x^2 = 16 cm^2
x=4 cm
8 cm * 16 cm * 20 cm = 2560 cm^3
Hungenahalli Sitaramarao Badarinath
Answered January 13, 2018
Let the length, breadth and height of the cuboid be 5x, 4x and 2x, respectively.
The total surface area of the cuboid is 2(LB +BH +HL) = 1216, or
(LB +BH +HL) = 608, or
(20x^2 + 8x^2 + 10x^2) = 608, or
38x^2 = 608, or
x^2 = 608/38 = 16, or x = 4.
The dimensions of the cuboid are 20 cm x 16 cm x 8 cm and so its volume = 2560 cc