A girl painted the outside of the cuboid shaped cabinet of measure 2 m × 3 m × 2.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
A girl painted the outside of the cuboid shaped cabinet of measure 2 m × 3 m × 2.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
The correct option is D 31 m²
The surface area of the bottom of the cuboid will be subtracted from the total surface area of the cabinet.
From the given figure,
Length 'l' of the cabinet = 2 m
Breadth 'b' of the cabinet = 3 m
Height 'h' of the cabinet = 2.5 m
Area of the bottom of cabinet = l × b
Since the cabinet is cuboidal in shape,
Total surface area of the cabinet = 2(l × b + b × h + h × l)
Area of the cabinet that was painted = (Total surface area of the cabinet) - (Area of bottom of the cabinet)
= 2(l × b + b × h + h × l) − l × b
= 2(b × h + h × l) + l × b
= 2 × (3 × 2.5 + 2.5 × 2) + 2 × 3 m²
= 2 × 12.5 + 6 m²
= 31 m²
Therefore the area of the cabinet that was painted is 31 m².
The surface area of the bottom of the cuboid will be subtracted from the total surface area of the cabinet.
From the given figure,
Length 'l' of the cabinet = 2 m
Breadth 'b' of the cabinet = 3 m
Height 'h' of the cabinet = 2.5 m
Area of the bottom of cabinet = l × b
Since the cabinet is cuboidal in shape,
Total surface area of the cabinet = 2(l × b + b × h + h × l)
Area of the cabinet that was painted = (Total surface area of the cabinet) - (Area of bottom of the cabinet)
= 2(l × b + b × h + h × l) − l × b
= 2(b × h + h × l) + l × b
= 2 × (3 × 2.5 + 2.5 × 2) + 2 × 3 m²
= 2 × 12.5 + 6 m²
= 31 m²
Therefore the area of the cabinet that was painted is 31 m².
