Question

1. Find the total surface area and lateral surface area for the solids with the following dimensions
Cuboid:
L=6cm
B=4cm
h=3cm​

Answer 1

Answer :-

• The total surface area of cuboid is 108cm².
• The lateral surface area of cuboid is 60cm².

Step-by-step explanation :

To Find :-

• The total surface area of cuboid
• The lateral surface area of cuboid

Solution :-

Given that,

• Length of cuboid = 6cm
• Breadth of cuboid = 4cm
• Height of cuboid = 3cm

According the question,

• The total surface area of cuboid,

As we know that,

Total surface area of cuboid = 2 ( lb + bh + hl ) sq. units,

=> 2 ( lb + bh + hl )

=> 2 ( 6*4 + 4*3 + 3*6 )

=> 2 ( 24 + 12 + 18 )

=> 2 ( 24 + 30 )

=> 2 ( 54 )

=> 2*54

=> 108

• The total surface area of cuboid is 108cm².

Now,

• The lateral surface area of cuboid,

As we know that,

Lateral surface area of cuboid = 2 [ ( l + b ) × h ] sq. units,

=> 2 [ ( l + b ) × h ]

=> 2 [ ( 6 + 4 ) × 3 ]

=> 2 [ 10 × 3 ]

=> 2 ( 30 )

=> 2*30

=> 60

• The lateral surface area of cuboid is 60cm.

Answer 2

Step-by-step explanation:

${\large{\bold{\rm{\underline{Let's\ understand\ the\ concept\ 1^{st}:-}}}}}$

★ This question says that there's a cuboid whose length is 6cm, breadth is 4cm, and the height is 3cm. Here we use the concept of total surface area of cuboid through which we will find out the T.S.A of cuboid by equating the given dimensions. One more concept is used, that is lateral surface area of cuboid through which we will find out the lateral surface area of cuboid. So let's do....!!!

${\large{\bold{\rm{\underline{Given\ that:-}}}}}$

$\sf {\bigstar Length\ of\ the\ cuboid\ =\ 6cm.}$

$\sf {\bigstar Breadth\ of\ the\ cuboid\ =\ 4cm.}$

$\sf {\bigstar Height\ of\ the\ cuboid\ =\ 3cm.}$

${\large{\bold{\rm{\underline{To\ find:-}}}}}$

★ In this question we have to find the total surface area and lateral surface area of cuboid ?

${\large{\bold{\rm{\underline{Using\ formula:-}}}}}$

$\star\;\underline{\boxed{\bf{\orange{Total\ surface\ area\ of\ cuboid\ =\ 2(lb\ +\ bh\ +\ hl).}}}}$

▪︎Where,

• L, denotes length.
• B, denotes breadth.
• H, denotes height.

___________________

$\star\;\underline{\boxed{\bf{\orange{Lateral\ surface\ area\ of\ cuboid\ =\ 2[(l\ +\ b) \times h].}}}}$

▪︎Where,

• L, denotes length.
• B, denotes breadth.
• H, denotes height.

${\large{\bold{\rm{\underline{Solution:-}}}}}$

★ Total surface area of cuboid = 108cm².

★ Lateral surface area of cuboid = 60cm.

${\large{\bold{\rm{\underline{Full\ solution:-}}}}}$

$\sf : \implies {Total\ surface\ area\ of\ cuboid\ =\ 2(lb\ +\ bh\ +\ hl)}$

$\sf : \implies {Total\ surface\ area\ of\ cuboid\ =\ 2(6 \times 4\ +\ 4 \times 3\ +\ 3 \times 6)}$

$\sf : \implies {Total\ surface\ area\ of\ cuboid\ =\ 2(24\ +\ 12\ +\ 18)}$

$\sf : \implies {Total\ surface\ area\ of\ cuboid\ =\ 2(54)}$

$\sf : \implies {Total\ surface\ area\ of\ cuboid\ =\ 2 \times 54}$

$\bf : \implies {\blue{Total\ surface\ area\ of\ cuboid\ =\ 108cm^2.}}$

∴ Hence, the total surface area of the cuboid is 108cm².

~Since, we also have to find out the lateral surface area of cuboid. So let's find out...!!!

$\sf : \implies {Lateral\ surface\ area\ of\ cuboid\ =\ 2[(l\ +\ b) \times h]}$

$\sf : \implies {Lateral\ surface\ area\ of\ cuboid\ =\ 2[(6\ +\ 4) \times 3]}$

$\sf : \implies {Lateral\ surface\ area\ of\ cuboid\ =\ 2[10 \times 3]}$

$\sf : \implies {Lateral\ surface\ area\ of\ cuboid\ =\ 2[30]}$

$\sf : \implies {Lateral\ surface\ area\ of\ cuboid\ =\ 2 \times 30}$

$\bf : \implies {\green{Lateral\ surface\ area\ of\ cuboid\ =\ 60cm^2.}}$

∴ Hence, the lateral surface of cuboid is 60cm².

${\large{\bold{\bf{\underline{\underline{More\ to\ know:-}}}}}}$

● Diagram of cuboid:

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf x\:cm}\put(7.7,6.3){\sf y\:cm}\put(11.3,7.45){\sf z\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {Total\ surface\ area\ of\ cuboid\ =\ 2(lb\ +\ bh\ +\ hl)}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {Lateral\ surface\ area\ of\ cuboid\ =\ 2[(l\ +\ b) \times h]}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {Volume\ of\ cuboid\ =\ (length \times breadth \times height)}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {Diagonal\ of\ cuboid\ =\ \sqrt{(l^2\ +\ b^2\ +\ h^2)}}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {Perimeter\ of\ cuboid\ =\ 4(length\ +\ breadth\ +\ height)}$