Mensuration
- If the volume of two right circular cones are in the ratio 4 : 1 and their diameter are in the ratio 5 : 4, then the ratio of their height is :
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V1 = r1²h1 V2 r2²h2 ⇒ 4 = 25 × h1 1 16 h2 ⇒ h1 = 16 × 4 = 64 or 64 : 25 h2 25 25 Correct Option: C
V1 = r1²h1 V2 r2²h2 ⇒ 4 = 25 × h1 1 16 h2 ⇒ h1 = 16 × 4 = 64 or 64 : 25 h2 25 25
- The volume of a conical tent is 1232 cu. m and the area of its base is 154 sq. m. Find the length of the canvas required to build the tent, if the canvas is 2m in width. (Take π = (22/7)
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πr² = 154
⇒ 22 × r² = 154 7 ⇒ r² = 154 × 722 ⇒ r = 7 metre 22 ∴ 1 πr²h = 1232 3 ⇒ h = 1232 = 8 3 154
⇒ h = 24 metre
Area of canvas curved surface area of cone = πrl
= πr √h² + r²= 22 × 7 = √24² + 4²sq. metre 7
= 22 × 25 = 550 sq. metre∴ Its length = 550 = 275 metre 2 Correct Option: D
πr² = 154
⇒ 22 × r² = 154 7 ⇒ r² = 154 × 722 ⇒ r = 7 metre 22 ∴ 1 πr²h = 1232 3 ⇒ h = 1232 = 8 3 154
⇒ h = 24 metre
Area of canvas curved surface area of cone = πrl
= πr √h² + r²= 22 × 7 = √24² + 4²sq. metre 7
= 22 × 25 = 550 sq. metre∴ Its length = 550 = 275 metre 2
- What is the volume of a cube (in cubic cm) whose diagonal measures 4√3 cm?
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Diagonal of a cube = √3 × side
⇒ 4√3 = √3 × side
∴ Side = 4 cm
∴ Volume of the cube = (side)³ = (4)³ = 64 cm³Correct Option: C
Diagonal of a cube = √3 × side
⇒ 4√3 = √3 × side
∴ Side = 4 cm
∴ Volume of the cube = (side)³ = (4)³ = 64 cm³
- From a solid cylinder of height 10 cm and radius of the base 6 cm, a cone of same height and same base is removed. The volume of the remaining solid is :
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Volume of the remaining solid
πr²h - 1 π r² h 3 = 2 πr²h = 2 π × 6 × 6 × 10 = 240π cu.cm. 3 3 Correct Option: A
Volume of the remaining solid
πr²h - 1 π r² h 3 = 2 πr²h = 2 π × 6 × 6 × 10 = 240π cu.cm. 3 3
- From a solid cylinder whose height is 12 cm and diameter 10cm, a conical cavity of same height and same diameter of the base is hollowed out. The volume of the remaining solid is approx imately (π = 22/7)
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Volume of solid cylinder = πr²h
Volume of cone = 1 π r² h 3 Difference = π r²h – 1 π r² h 3 = 2 π²h = 2 × 22 × 5 × 5 × 12 = 628.57 cu.cm. 3 3 7 Correct Option: C
Volume of solid cylinder = πr²h
Volume of cone = 1 π r² h 3 Difference = π r²h – 1 π r² h 3 = 2 π²h = 2 × 22 × 5 × 5 × 12 = 628.57 cu.cm. 3 3 7
