If the total surface area and lateral surface area of a solid cuboidal box of height 5cm is 340cm² and 180cm²,then the volume of the cuboidal box is???
Answers
lateral surface area Answer:
The volume of the is 400 cm³.
Step-by-step explanation:
In the context to the given question
we have to find the volume of the cuboid box
we know that;
Total surface area of cuboid = 2lb + 2lh +2bh
Lateral surface area cuboid = 2h (l+ b)
volume of cuboid = l x b x h
Given;
Height of the cuboid = 5 cm
Total surface area =340cm²
Lateral surface area cuboid = 180cm²
therefore;
Total surface area =340cm²
2lb + 2lh +2bh = 340
2 ( l b + l h + b
h ) = 340
by transposing method;
l b + l h + b h = 340/2
by putting value of h
l b + 5l + 5b = 170 [eq. 1]
Lateral surface area cuboid = 2h (l+ b)
180 = 2(5) (l + b)
(l + b) = 180/10
(l + b) = 18
l = (18 - b) [eq. 2]
by putting the value of l in [eq. 1]
b(18 - b) + 5(18 - b)+ 5b = 170
18b - b²+ 90 - 5b +5b = 170
18b - b² +90 = 170
By transposing method we get;
b² - 18b + 170 -90 =0
b² - 18b + 80 = 0
by factorizing
b² - 10b - 8b +80 = 0
b(b - 10) -8 ((b -10) = 0
(b-8)(b-10)=0
The value of b is 8 and 10cm
now; by putting the value in [ eq. 2 ], we get;
l = (18 -8) = 10cm
l = (18 - 10) =8cm
Volume of the cylinder will be = lx b x h
= 10 x 8 x 5
=400 cm³
Therefore, the volume of the is 400 cm³.