Question

Find the difference between TSA and LSA of a cuboid whose dimensions are 10cm x 5 cm x 3cm




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Answer 1

Diagram :

$\setlength{\unitlength}{0.5 cm}\begin{picture}(12,4)\thicklines\put(1,4){ . }\put(5.5,5.5){ A }\put(11.1,5.8){ B }\put(11.08,8.9){ C }\put(5.35,8.5){ D }\put(3.45,10.15){ E }\put(3.4,7.15){ F }\put(9.14,10.235){ H }\put(9.14,7.3){ G }\put(3.3,6.3){ 5\:cm }\put(7.75,6.2){ 10\:cm }\put(11.1,7.5){ 3\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

Given

↠ Dimensions of cuboid = 10 cm × 5 cm × 3 cm

To find

→ Difference b/w TSA and LSA of cuboid.

Solution

Formula to be used :

➻ TSA of cuboid = 2(lb + bh + hl)

➻ LSA of cuboid = 2(l + b) × h

Now at first to find TSA of cuboid :

➊ TSA of cuboid :

➔ TSA = 2(10 × 5 + 5 × 3 + 3 × 10)

➔ TSA = 2(50 + 15 + 30)

➔ TSA = 2 (95) cm²

➔ TSA = 190 cm²

∴ TSA of cuboid = 190 cm²

Now LSA of cuboid :

➋ LSA of cuboid :

➔ LSA = 2(10 + 5) × 3

➔ LSA = 2 × 15 × 3

➔ LSA = 90 cm²

∴ LSA of cuboid = 90 cm²

Now difference b/w TSA and LSA :

↠ Difference = TSA - LSA

↠ Difference = (190 - 90) cm²

↠ Difference = 100 cm²

Therefore, difference between TSA and LSA of cuboid = 100 cm²

Answer 2

Answer:

100 cm²

Step-by-step explanation:

Given that, length is 10cm, breadth is 5cm & height is 3 cm of cuboid.

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

Substitute the values,

Total surface area = 2(10 × 5 + 5 × 3 + 3 × 10)

= 2(50 + 15 + 30)

= 2(95)

= 190 cm² .................(1)

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

Substitute the values,

Lateral surface area = 2*3(10 + 5)

= 6(15)

= 90 cm² ...................(2)

Now,

Difference between total surface area and lateral surface is (1) - (2)

= (190 - 90) cm²

= 100 cm²

Hence, the difference between total surface area and lateral surface is 100 cm².