Right Circular Cylinder MCQ Quiz - Objective Question with Answer for Right Circular Cylinder - Download Free PDF

Given:

Internal radius of the pipe (r_pipe) = 3 cm

Rate of water flow from the pipe (speed of water) = x cm/second

Radius of the base of the cylindrical tank (R_tank) = 60 cm

Rise in water level in the tank (h_tank) = 15 cm

Time taken (T) = 5 minutes

Formula used:

Volume of water flowing out of the pipe in a given time = Area of cross-section of pipe × Speed of water × Time

Volume of water in cylindrical tank = πR²h

Calculation:

T = 5 minutes × 60 seconds/minute = 300 seconds

Volume of water flowed from pipe = Volume of water in the tank

Volume of water flowed from pipe = (π × r_pipe²) × (rate of flow) × Time

= π × (3 cm)² × (x cm/second) × (300 seconds)

= π × 9 × x × 300 cm³ = 2700πx cm³

Volume of water in the tank = π × R_tank² × h_tank

= π × (60 cm)² × (15 cm)

= π × 3600 × 15 cm³

= 54000π cm³

Equating the two volumes:

2700πx = 54000π

2700x = 54000

x = 54000 / 2700

x = 540 / 27

x = 20

∴ The correct answer is option 3.

Given:

Ratio of Volume of Cylinder to Volume of Cone = 25 : 16

Ratio of Height of Cylinder (H₁) to Height of Cone (H₂) = 3 : 4

Formula Used:

Volume of Cylinder (V_cyl) = πR₁²H₁

Volume of Cone (V_cone) = (1/3)πR₂²H₂

Calculation:

According to the given information:

V_cyl / V_cone = 25 / 16

(πR₁²H₁) / ((1/3)πR₂²H₂) = 25 / 16

Substitute the ratio of heights H₁/H₂ = 3/4, so H₁ = (3/4)H₂:

(πR₁²(3/4)H₂) / ((1/3)πR₂²H₂) = 25 / 16

⇒ (3/4)R₁² / ((1/3)R₂²) = 25 / 16

⇒ [(3/4)R₁² × 3] / (1 × R₂²) = 25 / 16

⇒ 9R₁² / 4R₂² = 25 / 16

⇒ R₁² / R₂² = (25 / 16) × (4 / 9)

R₁² / R₂² = 100 / 144

⇒ R₁ / R₂ = √(100 / 144)

⇒ R₁ / R₂ = 10 / 12

⇒ R₁ / R₂ = 5 / 6

∴ The ratio of the radii of the base of the cylinder and the cone is 5 : 6.

Given:

Number of people = 2,750

Water requirement per person per day = 100 L

Height of cylindrical tank (h) = 7 m

Diameter of cylindrical tank = 10 m

Radius of cylindrical tank (r) = Diameter / 2 = 10 / 2 = 5 m

Formula used:

Volume of cylinder = \(\pi r^2 h\)

Total water requirement per day = Number of people × Water requirement per person

Number of days water lasts = Volume of tank / Total water requirement per day

Calculation:

Volume of tank = \(\pi r^2 h\)

⇒ Volume = \(\pi × 5^2 × 7\)

⇒ Volume = \(\pi × 25 × 7 = 175\pi\) m³

Convert volume to liters (1 m³ = 1,000 L):

⇒ Volume in liters = \((175\pi × 1000)\) = 175,000\(\pi\) L

Using \(\pi \approx 22/7\):

⇒ Volume in liters = \((175,000 × 22/7 = 5,50,000)\) L

Total water requirement per day = 2,750 × 100 = 275,000 L

Number of days water lasts = \(\frac{\text{Volume of tank}}{\text{Total water requirement per day}}\)

⇒ Number of days = \(\frac{ 5,50,000}{275,000}\)

⇒ Number of days ≈ 2 days

∴ The correct answer is option (3).

Given:

Radius of the cylindrical vessel = 3.5 m

Volume of water taken out = 15400 liters = 15.4 m³

Formula Used:

Volume of a cylinder = π × radius² × height

Drop in water level = Volume taken out / (π × radius²)

Calculation:

Radius = 3.5 m

Volume taken out = 15.4 m³

π = 3.14

Drop in water level = Volume taken out / (π × radius²)

⇒ Drop in water level = 15.4 / (3.14 × 3.5²)

⇒ Drop in water level = 15.4 / (3.14 × 12.25)

⇒ Drop in water level = 15.4 / 38.465

⇒ Drop in water level ≈ 0.4 m

Convert to cm: 0.4 × 100 = 40 cm

The drop in the water level in the vessel is 40 cm.

Given:

Volume of the tank (V) = 12,320 m³

Radius of the base (r) = 14 m

Formula used:

Volume of a cylinder: V = πr²h

Where, h = depth of the tank

Calculation:

12,320 = (22/7) × 14 × 14 × h

⇒ h = 12,320 / [(22/7) × 14 × 14]

⇒ h = 12,320 / (44 × 14)

⇒ h = 12,320 / 616

⇒ h = 20 m

∴ The correct answer is option (1).

Given:

Height of the cylinder = 1 m 

Diameter = 140 cm = 1.4 m, so radius = 1.4/2 = 0.7 m

Concept used:

Total surface area of the cylinder = 2πrh + 2πr²

Calculation:

Total sheet required = 2πrh + 2πr² = 2πr(h + r)

⇒ 2 × 22/7 × 0.7 × (1 + 0.7)

⇒ 4.4 × 1.7

⇒ 7.48 m² 

∴ The correct answer is 7.48 m2. 

Given:

Volume ratio = 32 ∶ 9

Ratio of their heights is 8 ∶ 9

Area of the base of the second cylinder is 616 cm2

Concept Used:

Volume of cylinder = πr²h

Calculation:

Volume of the cylinder can be written as 32y and 9y

Height of the cylinder can be written as 8h and 9h

Since we know that the Volume of cylinder is Area of base × height

⇒ Volume of second cylinder = 616 × 9h

Let the radius of first cylinder be r

⇒ base area of first cylinder = πr²

Volume of first cylinder = πr² × 8h

Their ratios can be written as

⇒ 616 × 9h/ (πr² × 8h) = 9/32

Put π = 22/7

⇒  (22r2 × 8)/(616 × 9 × 7)/ = 32/9

⇒ r² = (616 × 9 × 32 × 7)/(9 × 22 ×  8)

⇒ r = 28

∴ Radius of first cylinder is 28 cm.

∴ Option 3 is the correct answer.

Given:

The ratio between the height and radius of the base of a cylinder is 7 ∶ 5.

Volume is 14836.5 cm3 

Formula used:

Volume of cylinder = πr²h

TSA of cylinder = 2πr(r + h)

Calculation:

Let the height be 7x and radius be 5x

According to the question,

Volume = π (5x)² × 7x

⇒ 14836.5 = (3.14)(25x²) × 7x

⇒ 14836.5 = (3.14)(25x2) × 7x

⇒ 175x³ = 14836.5/3.14

⇒ x3 = 4725/175

⇒ x3 = 27

⇒ x = 3

Now,

Radius = 5x =  5 × 3 = 15 cm

Height = 7x = 7 × 3 = 21 cm

For TSA of cylinder,

TSA = 2(3.14) × 15 × (15 + 21)

⇒ TSA = 6.28 × 15 × 36

⇒ TSA = 3391.2 cm² 

∴ The TSA of the cylinder is 3391.2 cm2.

Given:

Diameter of cylinder = 35 cm

Curved surface area = 3080 cm²

Formula used:

Radius = Diameter/2

Curved surface are of cylinder = 2πrh

Volume of cylinder = πr²h

where r = radius , h = height

Calculation: 

Diameter (d) = 35 cm

⇒ Radius = d/2

⇒ 35/2

 ⇒Radius = 17.5

Curved surface area of cylinder = 2πrh = 3080

⇒ 2 × 22/7 × 17.5 × h = 3080

⇒ h = 28 cm

Now Volume of cylinder = πr2h

⇒ 22/7 × (17.5)² × 28

⇒ 22 × 306.25 × 4

⇒ 26,950 cm³ 

∴ Volume of cylinder is 26,950 cm³.

Given:

Sum of radius and height of the cylinder = 39 cm

Total surface area of the cylinder = 1716 cm²

Concept used:

Total surface area of a cylinder = 2πr(h + r)

Volume = πr²h

Here,

r = radius

h = height

Calculation:

Let the radius and the height of the cylinder be r and h,

According to the question,

2πr(h + r) = 1716      ----(i)

(h + r) = 39      ----(ii)

Putting the value of eq (ii) in eq (i) we get,

2πr × 39 = 1716

⇒ 2πr = 1716/39

⇒ 2πr = 44

⇒ πr = 22

⇒ r = 22 × (7/22)

⇒ r = 7

So, radius = 7 cm

Now, by putting the value of r in the eq (ii) we get

h + 7 = 39

⇒ h = 32

So, height = 32 cm

Now, volume = (22/7) × 7² × 32

⇒ 22 × 7 × 32

⇒ 4928

So, volume of the cylinder = 4928 cm³

∴ The volume (in cm3) of the cylinder i 4928.

Given:

Curved surface area of cylinder = 308 cm²

Height = 14 cm

Formula used:

CSA (Curved surface area) = 2πrh

Volume = πr²h

Where r is radius and h is height

Calculation:

CSA = 2πrh

308 = 2 × (22/7) × r × 14

⇒ 308 = 88r

⇒ r = 7/2 = 3.5 cm

Volume = πr²h

⇒ Volume = (22/7) × (3.5)² × 14

⇒ Volume = 539 cm³ 

∴ Volume of the cylinder is 539 cm³

Given:

Width of canal  6 m 

Depth of canal = 1.5 m 

Speed of water in the canal = 10 km/hr

Time of irrigation is 30 min = 1/2 hr

8 cm of standing water is needed 

Concept Used:

The volume of a Cuboid = (Length × Breadth × Height) cubic units.

Water flow through canal = water required to irrigate

Calculation:

According to the question 

Length of water flow in 1/2 hr = l = 10 × (1/2) km

⇒ 5 km = 5000 m

⇒ Volume of water flown in 30 min = 6 × 1.5 × 5000

⇒ 45000 m³.

Now, According to the concept used

The volume of irrigated land = Area × Height

⇒ 45000 = Area × (8/100)

∴ The area of land of irrigation = 562500 m².

Given:

Radius of sphere = 8 cm

Radius of cylinder = 4 cm

The total surface area of the cylinder is half the surface area of the sphere

Formula used:

Total surface area of cylinder = 2πr(h + r)

Surface area of sphere = 4πr²

Calculation:

According to the question

The total surface area of the cylinder is half the surface area of the sphere

⇒ 2πr(h + r)/4πr² = 1/2

⇒ 2 × π × 4(h + 4)/(4 × π × 8²) = 1/2

⇒ 8(h + 4)/256 = 1/2

⇒ h + 4/32 = 1/2

⇒ h + 4 = 16

⇒ h = (16 – 4)

⇒ h = 12 cm

∴ The height of the cylinder is 12 cm

Given:

The internal radius (r) of a hollow cylindrical pipe = 14 m

External radius (R) = 21 m

Height (h) = 14 m

Formula Used:

Total Surface area of the hollow cylinder = 2πRh + 2πrh + 2π(R² - r²)

Calculation:

Total Surface Area = 2πRh + 2πrh + 2π(R2 - r2)

⇒ 2π ×  [h(R + r) + (R2 - r2)]

⇒ (44/7)[2 × 14(21 + 14) + (441 - 196)]

⇒ (44/7)[(14 × 35) + 245]

⇒ (44/7)[490 + 245]

⇒ 44 × 735/7

⇒ 44× 105

⇒ 4620

Hence, the correct answer is 4620 m2.

Given:

Curved surface area(CSA) of the cylinder = 484 cm²

Height(h) of the cylinder = 7 cm

Formula used:

CSA of cylinder = 2πrh

Volume(V) of cylinder = πr²h

r = radius of the base of the cylinder

Calculation:

2πrh = 484

⇒ 2 × \(\dfrac{22}{7}\) × r × 7 = 484

⇒ r = 11

V = πr2h

⇒ V = \(\dfrac{22}{7}\) × 11² × 7

⇒ V = 2662 

∴ Volume of the cylinder = 2662 cm³