MCQ: Right Circular Cylinder - SSC CGL MCQ

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 x 7x
⇒ 14836.5 = (3.14)(25x2) x 7x
⇒ 14836.5 = (3.14)(25x2) x 7x
⇒ 175x3 = 14836.5/3.14
⇒ x³ = 4725/175
⇒ x³ = 27
⇒ x = 3
Now,
Radius = 5x =  5 x 3 = 15 cm
Height = 7x = 7 x 3 = 21 cm
For TSA of cylinder,
TSA = 2(3.14) x 15 x (15 + 21)
⇒ TSA = 6.28 x 15x 36
⇒ TSA = 3391.2 cm² 

∴ The TSA of the cylinder is 3391.2 cm2.

Volume of the cylinder (V) = 180 cm³
Area of the base of the cylinder (A) = 30 cm²
Diameter of the cylinder base can be found from the area of the base using the formula A = πr2.
⇒ The radius (r) can be calculated from the area formula as √(A/π).
⇒ Therefore, the diameter is 2 × √(A/π).
Hence, the diameter of the cylinder is 

Given:

Radius of cylinder = 7 cm 
Height of the cylinder = 30 cm

Formula used  :

Area of base = π r² and
Total area of the 2 bases = 2 ×  π r²
Total surface area of cylinder = 2π r(h + r),
Where r = radius and h = height of cylinder

Calculations 

Required Ratio = 2π r² : 2π r(h + r)
⇒ Required Ratio = 2r : 2 (h + r)
⇒ Required Ratio = 2 × 7 : 2 (7 + 30)
⇒ Required Ratio = 7 : 37
∴ The required ratio = 7 : 37

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 x 1.5 x 5000
⇒ 45000 m³.
Now, According to the concept used
The volume of irrigated land = Area × Height
⇒ 45000 = Area x (8/100)
∴ The area of land of irrigation = 562500 m².

Given:

The radius and height of a right circular cylinder are r (in m).
The radius of the hemisphere is also equal to r (in m).
A right circular cylinder is surmounted in a solid hemisphere on its base.
The cost of painting is ₹2 per m2 and the total cost of painting the compound object is ₹1540,

Formula used:

(1) The curved surface area of the right circular cylinder = 2πrh
(2) The surface area for the base of the right circular cylinder = πr2

Where,

The radius and height of a right circular cylinder are r and h respectively.

(3) The surface area of the hemisphere = 2πr²

Where,
The radius of the hemisphere is also equal to r.

Calculation:

According to the question, the required figure is:

The radius and height of a right circular cylinder are r (in m).
The radius of the hemisphere is also equal to r (in m).

Now, 
The top circular surface area of the cylinder = πr²
The curved surface area of the cylinder = 2πrh

Since r = h,

Therefore, 
The curved surface area of the cylinder = 2πr²
The curved surface area of the hemisphere = 2πr²

Now, 
The total surface area of the compound object = πr² + 2πr² + 2πr² = 5πr²
The cost of painting = ₹2 per m² 
The total cost of painting the compound object = ₹1540,

Therefore, 
The total surface area of the compound object 

According to the question,

The height of the right circular cylinder = 7 m
∴ The height of the right circular cylinder is 7 m.

Given: 

The height of a solid cylinder is 35 cm.
The circumference of its base is 37 cm more than the radius.

Formula used:

Volume of cylinder = πr²h
Circumference of circle = 2πr

Calculations:

Circumference = 2πr
⇒ r + 37 = 2πr
⇒ 37 = 2πr - r
⇒ 37 = r(2π - 1)
⇒ 37 = r[(2 × 22/7) - 1]
⇒ 37 = r[44/7 - 1]
⇒ 37 = r(44 - 7)/7
⇒ 37 = (37/7)r
⇒ r = 7 cm

According to the question,
Vol. = π(7)2(35)
⇒ Vol. = (22/7)(7)2(35)
⇒ Vol. = (22)(7)(35)
⇒ Vol. = (154)(35) = 5390 cm³
∴ The volume of this cylinder is 5390 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) x 7² x 32
⇒ 22 x 7 x 32
⇒ 4928
So, volume of the cylinder = 4928 cm³
∴ The volume (in cm3) of the cylinder i 4928.

Given:

The total surface area of the cylinder = 462 sq. cm.
The curved surface area of the cylinder is one-third of its total surface area.

Formula used:

The curved surface area of cylinder = 2πrh
Total surface area of cylinder = 2πr2+ 2πrh = 2πr(r + h)
Where r and h are the radius and height of the cylinder respectively.

Calculation:

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

As the total surface area of cylinder = 462 sq. cm
⇒ 2πr(r + h) = 462      ----(1)
Curved surface area = 1/3 x (total surface area)
⇒ 1/3 x 462 = 154 sq. cm
⇒ Curved surface area = 2πrh = 154      ----(2)
Diving equation (1) by (2), we get
⇒ (r + h)/h = 3
⇒ r + h = 3h
⇒ r = 2h      ----(3)
From equation (2) and (3),
⇒ 2 x (22/7) x 2h x h = 154
⇒ h² = 49/4
⇒ h = 7/2
Putting the value of h in equation (3), we get
⇒ r = 2h = 2 x 7/2 = 7
Now, volume of cylinder = πr²h 
⇒ (22/7) x 7² x 7/2 =
⇒ 11 x 49 =539 sq. cm
∴ The volume of the cylinder is 539 sq. cm

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 x (22/7) × r × 14
⇒ 308 = 88r
⇒ r = 7/2 = 3.5 cm
Volume = πr2h
⇒ Volume = (22/7) x (3.5)² × 14
⇒ Volume = 539 cm³ 
∴ Volume of the cylinder is 539 cm³

Given:
The radius of a right circular cylinder is 7 cm.
Its height is thrice its radius.

Concept used:
Curved surface area of the cylinder = 2πrh

Calculation: 
Its height is thrice its radius.
So, height is 7 × 3 = 21 cm
The curved surface area of the cylinder is,
⇒ 2 x 22/7 x 7 x  21
⇒ 22  x 21 x 2 = 924 cm²

∴ The correct option is 1