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6. Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are: (1) length = 22 cm, breadth=12 cm and the height = 7.5 cm (ii) length = 24 m, breadth = 25 cm and the height = 6 m

Answer»

:-The volume, lateral surface area and the total surface area of the cuboid whose dimensions are:-(i) length = 22 cm, BREADTH = 12 cm, height = 7.5 cm(ii) length = 24 m, breadth = 25 cm, height = 6 mSolution:-(i) length = 22 cmbreadth = 13 cmheight = 7.5 cmFirstly let us calculate the volume of the cuboid.We know,Volume of cuboid = Length × breadth × heightTherefore,Volume = 22 × 12 × 7.5 ⇒ Volume = 1980 cm³∴ Volume of the cuboid is 1980 cm³.Now,Let us calculate lateral surface area.We know,LSA of a cuboid = 2(Length + Breadth) × HeightTherefore,LSA = 2(22 + 12) × 7.5⇒ LSA = 2 × 34 × 7.5 ⇒ LSA = 510 cm²∴ Lateral Surface Area of the cuboid is 510 cm².Now,Let us calculate the total surface area of the cuboid.We know,TSA of cuboid = 2(LB + BH + HL)Where L = Length, B = Breadth and H = HeightHence,TSA = 2[(22 × 12) + (12 × 7.5) + (7.5 × 22)]⇒ TSA = 2 [264 + 90 + 165]⇒ TSA = 2 × 519⇒ TSA = 1038 cm²∴ Total Surface Area of the cuboid is 1038 cm².________________________________(ii) Length = 24 mBreadth = 25 cm = 0.25 mHeight = 6 mVolume = L × B × H⇒ Volume = 24 × 0.25 × 6 ⇒ Volume = 36 m²∴ Volume of the cuboid is 36 m²LSA = 2(L + B) × Height⇒ LSA = 2(24 + 0.25) × 6⇒ LSA = 2 × 24.25 × 6⇒ LSA = 291 m²∴ Lateral Surface Area of the cuboid is 291 m².TSA = 2(LB + BH + HL)⇒ TSA = 2[(24 × 0.25) + (0.25 × 6) + (6 × 24)]⇒ TSA = 2[6 + 1.5 + 144]⇒ TSA = 2 × 151.5⇒ TSA = 303 m²∴ Total Surface Area of the cuboid is 303 m².________________________________



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