Question

3 cubes of
volume 27cm^3 are
joined
to end.
find
the
S.A
the
resulting cuboid.​

Answer 1

90 cm²

Explanation:

Given:

3 Cubes of volume 27 cm³ are joined end to end.

To find:

Total Surface Area (T.S.A)

Solution:

$\because$ Volume of cube = 27 cm³

$\therefore \textsf{Side of cube} = \sqrt[3]{27} \:\:\:\:\textsf{cm} ^{3} \implies 3 \:\:\: \text{cm}$

So the side of each cube is 3 cm.

$\because$All the cubes are joined end to end. (See In Attachment)

$\therefore$ Length(l) of new cuboid = (3+3+3)

= 9 cm

Breadth(b) = 3 cm

Height(h) = 3 cm

So, T.S.A = 2(lb+bh+lh)

= 2{(9×3)+(3×3)+(3×3)}

= 2(27 + 9 + 9) cm²

= 2(45) cm²

= 90 cm²

Additional Information:

Cube : Cube is a 3D shape which contains equal length, breadth and height. It have 8 vertex, 6 face and 12 edges.

e.g Cube and Dice etc.

Formula Related to Cube

Diagonal of cube = a√3 unit

T.S.A """"""""" = 6a² unit²

Volume """""""" = a³ unit³

[Where a is length of any equal side]

Cuboid : Cuboid is also a 3D shape which have similar properties like cube. But it's length breadth and height are not equal.

Formula Related to Cuboid.

Volume of Cuboid = l × b × h unit³

T.S.A of Cuboid= 2(lb+bh+lh) unit²

$\textsf{Diagonal of Cuboid} = \sqrt{l^2+b^2+h^2} \:\:\:\:\: \text{unit}$

[Where l , b and h are length, breadth and height of any Cuboid]

Answer 2

Answer:

90 cm²

Explanation:

Given:

3 Cubes of volume 27 cm³ are joined end to end.

To find:

Total Surface Area (T.S.A)

Solution:

\because∵ Volume of cube = 27 cm³

\therefore \textsf{Side of cube} = \sqrt[3]{27} \:\:\:\:\textsf{cm}$^{3}$ \implies 3 \:\:\: \text{cm}

So the side of each cube is 3 cm.

\because∵ All the cubes are joined end to end. (See In Attachment)

\therefore∴ Length(l) of new cuboid = (3+3+3)

= 9 cm

Breadth(b) = 3 cm

Height(h) = 3 cm

So, T.S.A = 2(lb+bh+lh)

= 2{(9×3)+(3×3)+(3×3)}

= 2(27 + 9 + 9) cm²

= 2(45) cm²

= 90 cm²

Additional Information:

Cube : Cube is a 3D shape which contains equal length, breadth and height. It have 8 vertex, 6 face and 12 edges.

e.g Cube and Dice etc.

Formula Related to Cube

Diagonal of cube = a√3 unit

T.S.A """"""""" = 6a² unit²

Volume """""""" = a³ unit³

[Where a is length of any equal side]

Cuboid : Cuboid is also a 3D shape which have similar properties like cube. But it's length breadth and height are not equal.

Formula Related to Cuboid.

Volume of Cuboid = l × b × h unit³

T.S.A of Cuboid= 2(lb+bh+lh) unit²

\textsf{Diagonal of Cuboid} = \sqrt{l^2+b^2+h^2} \:\:\:\:\: \text{unit}Diagonal of Cuboid=

l

2

+b

2

+h

2

unit

[Where l , b and h are length, breadth and height of any Cuboid]