If a brick has length, breadth and height in the ratio 1:2:3 and
the total surface area of the brick is 792 sq. m, then the volume
of the brick is
Answers
Answer:
Given:-
L= 1x
B= 2x
H= 3x
total surface area = 792 m²
Step-by-step explanation:
2 (lb + bh + hl) = total surface area of cuboidal brick
2 × 1x × 2x + 2x × 3x + 3x × 1x = 792
2×3x+6x+3x= 792
2×12x = 792
12x = 792 /2
12 x = 396
x = 396/12
x= 33
therefore :-
L= 1(33)=33
B= 2(33)=66
H= 3(33)=99
volume = l×b×h
33×66×99
215622 cm³
Step-by-step explanation:
length = 1x
breadth = 2x
height = 3x
Total surface area of a brick = 2(lb + bh + hl)
= 2[(1x)(2x) + (2x)(3x) + (3x)(1x)] = 792m²
= 2[2x² + 6x² + 3x²] = 792m²
= 2[11x²] = 792m²
= 22x² = 792m²
= x² = 792/22 m²
= x² = 36m
= x = 6m
hence,
length = 1(6) = 6m
breadth = 2(6) = 12m
height = 3(6) = 18m
Volume of the brick = length × breadth × height
= 6m × 12m × 18m
= 1296m³