Mensuration
- The radius of a cylinder is 10 cm and height is 4 cm. The number of centimetres that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is
-
View Hint View Answer Discuss in Forum
Let radius be increased byx cm. then Volume of cylinder = π(10 + x)² × 4
Again, let height be increased by x cm.
then Volume of cylinder = π × 10² (4 + x)
∴ π (10 + x)² × 4 = π (10)² (4 + x)
⇒ π(10 + x)² = 25 (4 + x)
⇒ 100 + 20x + x² = 100 + 25x
⇒ x² – 5x = 0
⇒ x (x – 5) = 0
⇒ x = 5 cmCorrect Option: A
Let radius be increased byx cm. then Volume of cylinder = π(10 + x)² × 4
Again, let height be increased by x cm.
then Volume of cylinder = π × 10² (4 + x)
∴ π (10 + x)² × 4 = π (10)² (4 + x)
⇒ π(10 + x)² = 25 (4 + x)
⇒ 100 + 20x + x² = 100 + 25x
⇒ x² – 5x = 0
⇒ x (x – 5) = 0
⇒ x = 5 cm
- The radii of the base of a cylinder and a cone are in the ratio √3 : √2 and their heights are in the ratio √2 : √3 . Their volumes are in the ratio of
-
View Hint View Answer Discuss in Forum
Volume of cylinder = πr1²h1 Volume of cone 1 πr2²h2 3 = 3. 
r1 
² h1 r2 h2 = 3 × √3 ² × √2 √2 √3 = 3 × √3 = 3√3 : √2 √2 Correct Option: B
Volume of cylinder = πr1²h1 Volume of cone 1 πr2²h2 3 = 3. r1 ² h1 r2 h2 = 3 × √3 ² × √2 √2 √3 = 3 × √3 = 3√3 : √2 √2
- The curved surface area and the total surface area of a cylinder are in the ratio 1 : 2. If the total surface area of the right cylinder is 616 cm², then its volume is :
-
View Hint View Answer Discuss in Forum
2πrh : 2πrh + 2πr&up2;= 1 : 2
⇒ 2πrh : 616 = 1 : 2⇒ 2πrh = 616 = 308 2
∴ 2πrh + 2πr² = 616
→ 308 + 2πr² = 616
⇒ 2πr² = 308⇒ r² = 308 × 7 = 49 22 × 2
⇒ r = 7∴ 2 × 22 × 7 × h = 308 2 ⇒ h = 308 = 7 44
∴ Volume of cylinder = πr²hCorrect Option: D
2πrh : 2πrh + 2πr&up2;= 1 : 2
⇒ 2πrh : 616 = 1 : 2⇒ 2πrh = 616 = 308 2
∴ 2πrh + 2πr² = 616
→ 308 + 2πr² = 616
⇒ 2πr² = 308⇒ r² = 308 × 7 = 49 22 × 2
⇒ r = 7∴ 2 × 22 × 7 × h = 308 2 ⇒ h = 308 = 7 44
∴ Volume of cylinder = πr²h
- The perimeter of the base of a right circular cylinder is ‘a’ unit. If the volume of the cylinder is V cubic unit, then the height of the cylinder is
-
View Hint View Answer Discuss in Forum
If the radius of base of cylinder be r units and its height be h units, then
2πr = a⇒ r = a units 2π
∴ Volume of cylinder = πr²h⇒ V = π × a² × h 4π² ⇒ h = 4π V units a² Correct Option: D
If the radius of base of cylinder be r units and its height be h units, then
2πr = a⇒ r = a units 2π
∴ Volume of cylinder = πr²h⇒ V = π × a² × h 4π² ⇒ h = 4π V units a²
- What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm ?
-
View Hint View Answer Discuss in Forum
Volume of sphere = 4 π × (6)³ cu.cm. 3
∴ Volume of cylinder = πr²h = π × (6)² × hNow, π × (6)² × h = 4 π × (6)³ cu.cm. 3 ⇒ π = 4 × 6 = 8 cm. 3 Correct Option: D
Volume of sphere = 4 π × (6)³ cu.cm. 3
∴ Volume of cylinder = πr²h = π × (6)² × hNow, π × (6)² × h = 4 π × (6)³ cu.cm. 3 ⇒ π = 4 × 6 = 8 cm. 3
