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

Given:

breadth = 5 m

diameter = 14 m

height = 24 m

Rate = Rs. 25/m

Formula used:

CSA(Cone) = 22/7 x r x l

l² = h² + r² 

r = radius of the cone/tent(here)

h = slant height

CSA = Curved Surface Area

Solution:

r = 14/2 = 7 m

l = \(\sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625}\)

l = 25 m

CSA = 22/7 x 7 x 25 

CSA = 550 m² 

Cost of cloth required = 550 x 25 = Rs. 13750

Hence, the correct option is 2.

Given:

Cost of polishing the total surface area of a solid cone = ₹ 5632

Rate of polishing = ₹ 0.50 per cm²

Circumference of the base of the cone = 176 cm

Formula used:

Total Surface Area (TSA) = Total Cost / Rate per cm²

Circumference of the base of a cone (C) = 2πr (where r is the radius of the base)

Total surface area of a cone (TSA) = πr(r + l) (where l is the slant height)

Relationship between height (h), radius (r), and slant height (l): l² = r² + h² (Pythagorean theorem)

Calculation:

TSA = Total Cost / Rate per cm²

TSA = 5632 / 0.50

TSA = 5632 × 2

TSA = 11264 cm²

Circumference (C) = 2πr

176 = 2 × (22/7) × r

176 = (44/7) × r

r = (176 × 7) / 44

r = 4 × 7 = 28 cm

Total Surface Area (TSA) = πr(r + l)

11264 = (22/7) × 28 × (28 + l)

11264 = 22 × 4 × (28 + l)

11264 = 88 × (28 + l)

28 + l = 11264 / 88

28 + l = 128

l = 128 - 28 = 100 cm

Using the Pythagorean theorem: l² = r² + h²

100² = 28² + h²

10000 = 784 + h²

h² = 10000 - 784

h² = 9216

h = √9216 = 96

∴ The correct answer is option 4.

Given:

Ratio of volumes of two cones = 3 : 2

Ratio of radii of the two cones = 3 : 4

Formula:

The volume of a cone is given by the formula:

V = (1/3)πr²h

Solution:

Let's assume the radii of the two cones are 3x and 4x, where x is a common factor.

So, the ratio of their radii is 3x : 4x.

The volume of the first cone (V1) can be expressed as:

V1 = (1/3)π(3x)²h1

V1 = (1/3)π9x²h1

The volume of the second cone (V2) can be expressed as:

V2 = (1/3)π(4x)2h1

V2 = (1/3)π16x2h1

Given that the ratio of volumes of the two cones is 3 : 2, we have:
V1/V2 = 3/2

9x​2h1/16x​2h2 = 3/2

h1 / h2 = 48x²/18x​2

h1/h2 = 8/3

Therefore, the ratio of the heights of the two cones is 8 : 3.

Given:

Radius (r) = 5 cm

Slant height (l) = 16 cm

Formula used:

Total surface area of cone = πr(r + l)

Where, π = 22/7

Calculation:

Total surface area = (22/7) × 5 × (5 + 16)

⇒ Total surface area = (22/7) × 5 × 21

⇒ Total surface area = (22 × 5 × 21)/7

⇒ Total surface area = (2310)/7

⇒ Total surface area = 330 cm²

∴ The correct answer is option (3).

Given:

The circumference of the base of 10 m high conical tent is 44 meter.

Concept used: 

Circumference of circle = 2πr

Curved surface Area of cone = πrl 

Calculation: 

⇒ 2πr = 44

⇒ r = 7 m

Now,

l = \(\sqrt{h^2+r^2} = \sqrt{100 + 49}\) = 12.2

Area = π × 7 × 12.2 = 268.5 m2

∴ The area of the canvas used in making the tent is 268.5 m2.

Given:

The curved surface area of the cone = 2 × base area of cone

Concepts used:

Formula used

Slant height (l) of cone = √r² + h²

CSA of cone = πrl

Calculation:

Let the radius of the cone be r units.

⇒ πrl = 2πr2

⇒ l = 2r

⇒ r = 6√3/2

⇒ r = 3√3

Slant height (l) of cone = √r2 + h2

⇒ 6√3² = 3√3² + h2

⇒ h2 = 108 - 27 = 81

⇒ h = 9 cm

∴ The answer is 9 cm.

Given:

Diameter of the cylinder = 14 cm

Height of the cylinder = 2 cm

π = 22/7

Formula used:

The curved surface area of a cylinder = 2πrh

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

Solution:

Curved surface area = 2πrh

= 2 × 22/7 × 7 × 2

= 44 × 2

= 88 cm²

Total surface area = 2πr(r + h)

= 2 × 22/7 × 7(7 + 2)

= 44 × 9

= 396 cm²

Sum of the surface areas = 88 cm² + 396 cm²

= 484 cm²

∴ Option 1 is the correct answer.

Given data:

Cone: height (h) = 8 cm, radius (r) = 4 cm

Rectangular block: length = 8 cm, breadth = 6 cm, height = 4 cm

Concept Used:

The volume of a cone = 1/3πr²h,

the volume of a rectangular block = length × breadth × height.

The percentage waste = ((Volume of block - Volume of cone)/Volume of block) × 100%.

Calculation:

⇒ Volume of cone = 1/3π(4)² × (8) = 134.041 cm³

⇒ Volume of block = 8 × 6 × 4 = 192 cm³

⇒ Waste = 192 - 134.041 = 57.959 cm³

⇒ Percentage waste = (57.959/192) × 100% ≈ 30%

Therefore, the approximate percentage of wood wasted is 30%.

Given:

Height of cone = 15 cm

Radius of cone = 7 cm

Formula:

Volume of cone = πr²h/3

Calculation:

Volume of cone

⇒ [1/3] × π × r² × h

⇒ [1/3] × [22/7] × 7 × 7 × 15

⇒ 22 × 7 × 5

⇒ 770 cm³

Given:

Height of tent (H) = 10 m

Base diameter (D) = 48 m

Formula used:

The curved surface area of the cone = π × R × l

Where, l = √(H² + R²) 

R = radius ; l = slant height

Calculation:

Base diameter (D) = 48 m

Base radius (R) = 48/2 = 24 m

Slant height (l) = √(H2 + R2)

⇒ √{(10)2 + (24)2}

⇒ √{100 + 576} = √676

⇒ 26 m

The curved surface area of the cone = π × R × l

⇒ π × 24 × 26 = 624 π m² 

∴ The correct answer is 624 π m2. 

Given:

Radius = 14m

Height = 48m

Width of the canvas = 8m

Formula used:

Pythagoras Theorem,

Slant height2 = Radius2 + Height2

Curved Surface area of the cone = π r l [ where r is radius and l is slant height]

Calculation:

Slant height2 = Radius2 + Height²

l² = 14² + 48²

l = \(\sqrt{196+2304}\)

l = \(\sqrt{2500}\)

l = 50cm

Curved Surface area of the cone = π r l

= \(\frac{22×14×50}{7}\)

= 2200m²

Canvas required if the width is 8m,

= 2200 / 8

= 275

Answer is 275.

Additional InformationVolume  of the cone = \(\frac{1}{3}\)πr2h

Given

The circumference of the base = 33 cm

Height solid cone = 16 cm

Calculation:

Circumference of the base of a cone = 2πr

⇒ 2πr = 33

⇒ 2 × (22/7) × r = 33

⇒ r = 21/4

Volume of cone = (1/3) πr²h

⇒ (1/3) × (22/7) × (21/4) × (21/4) × 16

⇒ 21 × 22 = 462 cm³

∴ The volume of the cone is 462 cm³.

Given

Diameter of conical cap = 24 cm

Height of conical cap = 16 cm

Formula used

Curved surface area of cone = πrl

l² = r² + h²

Where, l = slant height of the cone

r = radius of the cone

h = height of the cone

Calculation

Diameter of conical cap = 24 cm

Radius of conical cap = 12 cm

Now, l2 = r2 + h²

⇒ l² = (12² + 16²)

⇒ l² = (144 + 256)

⇒ l² = 400 cm²

⇒ l = 20 cm

The curved surface area of the cone = πrl

⇒ (\(\frac{22}{{7}}\) × 12 × 20) cm²

⇒ \(\frac{5280}{{7}}\) cm²

The cost of painting the surface of the cap

⇒ Rs. (\(\frac{5280}{{7}}\) × 70/100)   [1 rupee = 100 paisa]

⇒ Rs. 528

∴ The cost of painting the surface of the cap is Rs. 528.

Given:

Height of cone = 20 cm

Slant height of cone = 25 cm

Formula:

Volume of cone = [1/3]πr²h

l² = r² + h²

Calculation:

According to the question

25² = r² + 20²

⇒ 625 = r² + 400

⇒ r² = 625 – 400

⇒ r² = 225

⇒ r = 15

Given:

The radius of the base of a conical tent is 9 m and its height is 12 m

Concept used:

Curved surface area of a cone = π × Radius × Slant Height

Slant height = \(\sqrt{Radius^2 + Height^2}\)

Calculation:

Slant height of the conical tent = \(\sqrt{12^2 + 9^2}\) = 15 cm

Hence, the curved surface area of the conical tent = π × 9 × 15 = 135π m²

Thus, the cost of the material = (135π × 100) ÷ π = Rs. 13,500

∴ The cost of the material is Rs. 13,500.