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

Given:

Volume of cylinder (V) = 5852 cm³

Height of cylinder (h) = 38 cm

Value of \(\pi = \frac{22}{7}\)

Formula used:

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

Total Surface Area of a solid cylinder = \(2\pi r(r + h)\)

Where r = radius

Calculations:

First, find the radius (r) using the volume formula:

V = \(\pi r^2 h\)

5852 = \(\frac{22}{7} \times r^2 \times 38\)

⇒ r² = \(\frac{5852 \times 7}{22 \times 38}\)

⇒ r² = \(\frac{40964}{836}\)

⇒ r² = 49

⇒ r = \(\sqrt{49}\)

⇒ r = 7 cm

Now, calculate the Total Surface Area (TSA) of the cylinder:

TSA = \(2\pi r(r + h)\)

⇒ TSA = \(2 \times \frac{22}{7} \times 7 \times (7 + 38)\)

⇒ TSA = \(2 \times 22 \times 45\)

⇒ TSA = \(44 \times 45\)

⇒ TSA = 1980 cm²

∴ The total surface area of the solid cylinder is 1980 cm².

Find Length and Breadth of the Rectangle

Let length= 9x, breadth= 5x.

Perimeter = 2(9x + 5x) = 280

2(14x) = 280 ⟹ 28x = 280 ⟹ x = 10

Thus,

Length = 9x = 90 cm, Breadth = 5x = 50 cm

Area of rectangle = 90 × 50 = 4500 cm².

The top surface of the cylinder is a circle with area πr²

Given:

πr2 = 4500 ⟹ r2 = 4500π

Given: Radius r = 120% of height h, so:

r = 1.2h ⟹ h = r / 1.2 = 5r / 6

Now, let's find the Curved Surface Area of Cylinder:

Curved surface area = 2πrh 

Substitute, h = 5r / 6:

CSA = 2πr(5r/6) = 10πr2 / 6 = 5πr2 / 3

Since πr2 = 4500:

CSA = 5 x 4500 / 3 = 7500 cm2

Thus, the correct answer is 7500 cm2.

Given:

Original radius of the cylinder = r

Original height of the cylinder = h

New radius = 50% decrease = r - 0.5r = 0.5r

New height = 50% increase = h + 0.5h = 1.5h

Formula Used:

Volume of a cylinder = πr²h

Calculation:

Original volume = πr²h

New volume = π(0.5r)²(1.5h)

⇒ New volume = π(0.25r²)(1.5h)

⇒ New volume = 0.375πr²h

Decrease in volume = Original volume - New volume

⇒ Decrease = πr²h - 0.375πr²h

⇒ Decrease = (1 - 0.375)πr²h

⇒ Decrease = 0.625πr²h

Percentage decrease = (Decrease / Original volume) × 100

⇒ Percentage decrease = (0.625πr²h / πr²h) × 100

⇒ Percentage decrease = 0.625 × 100

⇒ Percentage decrease = 62.5%

The volume will be decreased by 62.5%.

Given:

Length of rectangular sheet = 31.4 cm

Breadth of rectangular sheet = 10 cm

Formula used:

Circumference of the base of the cylinder = Length of the sheet

Height of the cylinder = Breadth of the sheet

Volume of the cylinder = π × r² × h

Where, r = radius of the base, h = height

Calculation:

Length of the sheet = Circumference of the base = 2πr

⇒ 31.4 = 2 × 3.14 × r

⇒ r = 31.4 / (2 × 3.14)

⇒ r = 5 cm

Height of the cylinder = Breadth of the sheet = 10 cm

Volume of the cylinder = π × r² × h

⇒ Volume = 3.14 × (5)² × 10

⇒ Volume = 3.14 × 25 × 10

⇒ Volume = 785 cm³

∴ The correct answer is option (1).

Calculation

So, [r – 3] / [r + 4] = 1 /2

Or, 2r – 6 = r + 4

r = 10

So, Radius of cylinder is 10 – 3 = 7 and 10 + 4 = = 14 respectively.

Height of cylinder is 14 and 28 respectively.

So, volume is cylinder = [22/7] × 14 × 7 × 7 = 2156

Volume of cylinder = [ 22/7] × 14 × 14 × 28 = 17248

So, difference is 17248 – 2156 = 15092

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:

Dimensions of the metallic rectangular block is 112 cm × 44 cm × 25 cm

Radius of the cylinder = 35 cm

Concept used:

Volume of a cuboid = l × b × h

Volume of a cylinder = πr²h

Curved surface area of the cylinder = 2πrh

Here,

l = length

b = breadth

h = height

r = radius

h = height

Calculation:

Let the height of the cylinder be h

According to the question,

112 × 44 × 25 = (22/7) × 35² × h

⇒ (112 × 44 × 25 × 7)/(22 × 35 × 35) = h

⇒ h = 32

So, the height of the cylinder = 32 cm

Now,

Curved surface area of the cylinder = 2 × (22/7) × 35 × 32

⇒ 44 × 5 × 32

⇒ 7040

∴ The curved surface area (in cm2) of the cylinder is 7040.