Find the lateral surface area and the total surface area of a cuboid whose length = 16cm, breadth = 12 cm and height = 8 cm About the author Samantha
Answer: Please mark me as the Brainliest Step-by-step explanation: Lateral Surface area = 2 height(length + breadth) = 2. (8) (16 + 12) = 16 × 28 = 448 cm² Total Surface area = 2 (Length x Breadth + breadth x height + Length x height) = 2 [ (16).(12) + (12).(8) + (16).(8) ] = 2 [ 192 + 96 + 128 ] = 2 × 416 = 832 cm² Lateral Surface Area of Cuboid = 448 cm² Total Surface Area of Cuboid = 832 cm² Reply
[tex]\large\sf\underline{Given\::}[/tex] Length of the cuboid = 16 cm. Breadth of the cuboid = 12 cm. Height of the cuboid = 8 cm. [tex]\large\sf\underline{To\:find\::}[/tex] Total surface area ( TSA ) of the cuboid Lateral surface area ( LSA ) of the cuboid [tex]\large\sf\underline{Solution\::}[/tex] We know , [tex]\large{\mathfrak{TSA \:of\:the\:cuboid\:=\:2(lb+bh+lh)}}[/tex] where : l stands for [tex]{\sf{{\pink{Length}}}}[/tex]. b stands for [tex]{\sf{{\pink{breadth}}}}[/tex]. h stands for [tex]{\sf{{\pink{height}}}}[/tex]. Substituting the given values in the formula : [tex]\sf:\implies\:TSA\:=\:2[(16 \times 12) +(12 \times 8) +(16 \times 8) ][/tex] [tex]\sf:\implies\:TSA\:=\:2[192 + 96 + 128][/tex] [tex]\sf:\implies\:TSA\:=\:2[416][/tex] [tex]\sf:\implies\:TSA\:=\:2 \times 416[/tex] [tex]\small{\underline{\boxed{\mathrm\red{:\implies\:TSA\:=832\:sq.cm}}}}[/tex] ★ ___________________________ Now, [tex]\large{\mathfrak{LSA \:of\:the\:cuboid\:=\:2h(l+b)}}[/tex] where : l stands for [tex]{\sf{{\pink{Length}}}}[/tex]. b stands for [tex]{\sf{{\pink{breadth}}}}[/tex]. h stands for [tex]{\sf{{\pink{height}}}}[/tex]. Substituting the given values in the formula : [tex]\sf:\implies\:LSA\:=\:2 \times 8[16+12][/tex] [tex]\sf:\implies\:LSA\:=\:2 \times 8[28][/tex] [tex]\sf:\implies\:LSA\:=\:2 \times 8 \times 28[/tex] [tex]\sf:\implies\:LSA\:=\:16 \times 28[/tex] [tex]\small{\underline{\boxed{\mathrm\red{:\implies\:LSA\:=448\:sq.cm}}}}[/tex] ★ ___________________________ !! Hope it helps !! Reply
Answer:
Please mark me as the Brainliest
Step-by-step explanation:
Lateral Surface area = 2 height(length + breadth)
= 2. (8) (16 + 12)
= 16 × 28
= 448 cm²
Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)
= 2 [ (16).(12) + (12).(8) + (16).(8) ]
= 2 [ 192 + 96 + 128 ]
= 2 × 416
= 832 cm²
Lateral Surface Area of Cuboid = 448 cm²
Total Surface Area of Cuboid = 832 cm²
[tex]\large\sf\underline{Given\::}[/tex]
[tex]\large\sf\underline{To\:find\::}[/tex]
[tex]\large\sf\underline{Solution\::}[/tex]
We know ,
[tex]\large{\mathfrak{TSA \:of\:the\:cuboid\:=\:2(lb+bh+lh)}}[/tex]
where :
Substituting the given values in the formula :
[tex]\sf:\implies\:TSA\:=\:2[(16 \times 12) +(12 \times 8) +(16 \times 8) ][/tex]
[tex]\sf:\implies\:TSA\:=\:2[192 + 96 + 128][/tex]
[tex]\sf:\implies\:TSA\:=\:2[416][/tex]
[tex]\sf:\implies\:TSA\:=\:2 \times 416[/tex]
[tex]\small{\underline{\boxed{\mathrm\red{:\implies\:TSA\:=832\:sq.cm}}}}[/tex] ★
___________________________
Now,
[tex]\large{\mathfrak{LSA \:of\:the\:cuboid\:=\:2h(l+b)}}[/tex]
where :
Substituting the given values in the formula :
[tex]\sf:\implies\:LSA\:=\:2 \times 8[16+12][/tex]
[tex]\sf:\implies\:LSA\:=\:2 \times 8[28][/tex]
[tex]\sf:\implies\:LSA\:=\:2 \times 8 \times 28[/tex]
[tex]\sf:\implies\:LSA\:=\:16 \times 28[/tex]
[tex]\small{\underline{\boxed{\mathrm\red{:\implies\:LSA\:=448\:sq.cm}}}}[/tex] ★
___________________________
!! Hope it helps !!