Question

a closed metal trunk is 2 meters long 1.5 metre broad and 1 metre high. find its total surface area​

Answer 1

$\huge\bold{QUESTION}$

❥A Closed Metal Trunk Is 2 Meters Long 1.5 Metre Broad And 1 Metre High. Find Its Total Surface Area

$\huge\bold{ANSWER}$

GIVEN:-

A METAL TRUNK HAVE

Length=2m (l)

Breadth=1.5m (b)

Height=1m (h)

TO FIND:-

Total Surface Area of Trunk

SOLUTION:-

As we know, the metal trunk is in the form of cuboid.

Total Surface Area is the sum of areas of all surfaces of the solid.

• For a cube and cuboid, it is the sum of all 6 surfaces
• For a cyclinder, it is the sum of areas of 2 circular bases and its curved surface area
• For a cone, it is the sum of it's circular base area and curved surface area

From above

We can say,

Total Surface area of Cuboid=

=[sum of area of top and bottom suface]+[sum of areas of front and back surfaces]+[sum of left and right surfaces]

=[lb+lb]+[bh+bh]+[lh+lh]

=2lb+2bh+2lh

=2(lb+bh+lh)

Putting Values In Formula

Total Surface Area of Trunk

=2[(2×1.5)+(1.5×1)+(2×1)]

=2[3+1.5+2]

=2×6.5

=13m²

. ˙ . Therefore, Total Surface Area of Cuboidal Trunk is 13m²

ADDITIONAL INFORMATION

SOME BASIC MENSURATIONAL FORMULAS:-

➜Square (for side a)

• Area=a²
• Perimeter=4a

➜Rectangle (for length l and breadth b)

• Area=l × b
• perimeter=2 ( l + b)

➜Circle (for radius r)

• Area=πr²
• Circumference=2 π r

➜Cube (for side a)

• Volume= a³
• Lateral Surface Area=4 a²
• Total Surface Area=6 a²

➜Cuboid (for length l, breadth b and height h)

• Volume=l × b × h
• Lateral Surface Area=2 h (l + b)
• Total Surface Area= 2 (lb +bh +hl)

➜Sphere (for radius r)

• Volume=(4/3) π r³
• Curved Surface Area= 4 π r²
• Total Surface Area= 4 π r²

➜Hemisphere (for radius r)

• Volume=(⅔) π r³
• Curved Surface Area=2 π r²
• Total Surface Area=3 π r²

➜Cylinder (for radius r and height h)

• Volume=π r² h
• Curved Surface Area=2π r h
• Total Surface Area= 2πrh + 2πr²

➜Cone ( for radius r and Height h)

• Volume= (⅓) π r² h
• Curved Surface Area= π r l
• Total Surface Area= πr (r + l)

Answer 2

$\huge{\underline{\underline{\mathrm{\red{AnswEr}}}}}$

Given:-

A METAL TRUNK HAVE

Length=2m (l)

Breadth=1.5m (b)

Height=1m (h)

To find:-

Total Surface Area of Trunk

Solution:-

As we know, the metal trunk is in the form of cuboid.

Total Surface Area is the sum of areas of all surfaces of the solid.

• For a cube and cuboid, it is the sum of all 6 surfaces
• For a cyclinder, it is the sum of areas of 2 circular bases and its curved surface area
• For a cone, it is the sum of it's circular base area and curved surface area

From above

We can say,

Total Surface area of Cuboid=

⇒[sum of area of top and bottom suface]+[sum of areas of front and back surfaces]+[sum of left and right surfaces]

⇒[lb+lb]+[bh+bh]+[lh+lh]

⇒2lb+2bh+2lh

⇒2(lb+bh+lh)

Putting Values In Formula

Total Surface Area of Trunk

↝2[(2×1.5)+(1.5×1)+(2×1)]

↝2[3+1.5+2]

↝2×6.5

↝13m²

. ˙ . Therefore, Total Surface Area of Cuboidal Trunk is 13m²$.$