Question

The base of a rectangular solid is 4 ft long and 3 ft wide. Find the volume and total surface area of the solid if its diagonal is sqrt of 41 ft

Answer 1

let the height be h 
√(4^2 + 3^2 + h^2) = √41 
square both sides 
16 + 9 + h^2 = 41 
h^2 = 16 
h = 4 

V=4x3x4 = 48ft cube

Answer 2

Volume and total surface area of the solid is 48 ft³ and 80 ft²

Given that;

Length of a rectangular solid = 4 ft

Width of a rectangular solid = 3 ft

Diagonal = √41 ft

Find:

Volume and total surface area of the solid

Computation:

√l² + b² + w² = √41

4² + 3² + w² = 41

16 + 9 + w² = 41

25 + w² = 41

w² = 41 - 25

w = 4

Volume of the solid = lbh

Volume of the solid = (4)(3)(4)

Volume of the solid = 48 ft³

Surface area of the solid = 2[lb + bh + hl]

Surface area of the solid = 2[(4)(3) + (3)(4) + (4)(4)]

Surface area of the solid = 2[12 + 12 + 16]

Surface area of the solid = 2[40]

Surface area of the solid = 80 ft²

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