Answer:
Step-by-step explanation:
Question 01
The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88cm².The volume of the cuboid is?
Let the length of the cuboid =x, breadth =2x, height =3x
Total surface area of a cuboid of length (l), breadth (b) and height (h) =2(l × b + b × h +l ×h)
Given, total surface area of the cuboid =88cm²
2(x × 2x + 2x × 3x + x × 3x) = 88cm²
22x² = 88
x² = 4 ⇒ x = 2
Hence, the length of the cuboid = x =2cm, breadth = 2x = 4cm, height = 3x = 6cm
Volume of a cuboid =l × b × h
So, the volume of the cuboid with length = 2cm, breadth = 4cm and height = 6cm = 2 × 4 × 6 = 48cm³
Question 02
Three solid cubes of sides 1cm, 6cm and 8cm respectively are melted to form a new cube. Find the surface area of the cube
Answer
Given a₁ = 1 cm a₂ = 6 cm a₃ = 8 cm
the volume of a cube V = a³
Volume of cube 1, V₁ = (a₁)³ = 1³ = 1 cm³
Volume of cube 2, V₂ = (a₂)³ = 6³ = 216 cm³
Volume of cube 3, V₃ = (a₃)³ = 8³ = 512 cm³
∴ Volume of new cube = 1 + 216 + 512 = 729 cm³
edge of bigger cube = ∛(729) = 9
Surface area of cube =6 × a² = 6 × 9 × 9 = 46 cm²
Question 03
Find the volume and surface area of a cube who's edge is 5 cm
Volume = a³ = 5³ = 125 cm³
TSA of a cube = 6 × a²
Surface area = 6 × 5 × 5
Surface area = 150 cm²
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Verified answer
Answer:
Step-by-step explanation:
Question 01
The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88cm².The volume of the cuboid is?
Answer:
Let the length of the cuboid =x, breadth =2x, height =3x
Total surface area of a cuboid of length (l), breadth (b) and height (h) =2(l × b + b × h +l ×h)
Given, total surface area of the cuboid =88cm²
2(x × 2x + 2x × 3x + x × 3x) = 88cm²
22x² = 88
x² = 4 ⇒ x = 2
Hence, the length of the cuboid = x =2cm, breadth = 2x = 4cm, height = 3x = 6cm
Volume of a cuboid =l × b × h
So, the volume of the cuboid with length = 2cm, breadth = 4cm and height = 6cm = 2 × 4 × 6 = 48cm³
Question 02
Three solid cubes of sides 1cm, 6cm and 8cm respectively are melted to form a new cube. Find the surface area of the cube
Answer
Given a₁ = 1 cm a₂ = 6 cm a₃ = 8 cm
the volume of a cube V = a³
Volume of cube 1, V₁ = (a₁)³ = 1³ = 1 cm³
Volume of cube 2, V₂ = (a₂)³ = 6³ = 216 cm³
Volume of cube 3, V₃ = (a₃)³ = 8³ = 512 cm³
∴ Volume of new cube = 1 + 216 + 512 = 729 cm³
edge of bigger cube = ∛(729) = 9
Surface area of cube =6 × a² = 6 × 9 × 9 = 46 cm²
Question 03
Find the volume and surface area of a cube who's edge is 5 cm
Answer:
Volume = a³ = 5³ = 125 cm³
TSA of a cube = 6 × a²
Surface area = 6 × 5 × 5
Surface area = 150 cm²