Question

A cubical box has each edge 10cm and other cubodial box is 12.5cm long, 10cm wide and 8cm high.
(1)Which box has the greater lateral surface area and by how much?
(2) Which box has the smaller total surface area and by how much?
if anyone answered it I will rate 5 star​

Answer 1

Answer:

Step-by-step explanation:

(i) Lateral surface area of cube = 4edge  

2

 

=4(10)  

2

 

=400

​  

 

lateral surface area of cuboid =2h(l+b)

2×8(12.5+10)

=16×22.5

=360

​  

 

So, the lateral surface area of the cube is larger by (400−360=40)cm  

2

 

(ii) Total surface area of cube = 6edge  

2

 

=6(10)  

2

 

=600

​  

 

lateral surface area of cuboid =2(lb+bh+hl)

2(12.5×10+10×8+8×12.5)

=2(125+80+100)

=610

​  

 

So, the total surface area of cuboid is larger by (610−600=10) cm  

2

Answer 2

Step-by-step explanation:

(1)

Formula to find the LSA/ Lateral Surface Area of a cube is = 4s²

So the equation will be:

4 x 10²

4 x 10 x 10

4 x 100

=400

Formula to find the LSA/ Lateral Surface Area of a cuboid is = 2h( l+ b)

So the equation will be:

2 x 8 x ( 12.5 + 10 )

2 x 8 x 22.5

16 x 22.5

= 360

Therefore the box which has greater lateral surface area/LSA is the cubical box.

(2)

The formula to find the TSA/ Total Surface Area of a cube is = 6s²

So the equation will be:

6 x 10²

6 x 10 x 10

6 x 100

= 600

The formula to find the TSA/ Total Surface Area of a cuboid is = 2( lb + bh +

                                                                                                                           hl)    

So the equation will be:

2( 12.5 x 10 + 10 x 8 + 8 x 12.5)

2(125 + 80 + 100)

2 x 305

= 610

Therefore the cube has smaller Total Surface Area/TSA.

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