Area And Volume - 3D Test

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Area And Volume - 3D Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

The lateral surface area of a right circular cylinder with base radius 7 cm and height 20 cm is

A
880 cm²

B
404 cm²

C
240 cm²

D
none of these

Solution

Radius of the lateral surface area of a right circular cylinder = 7 cm
Height of the lateral surface area of a right circular cylinder = 20 cm
Thelateral surface area of a right circular cylinder =
=
=
Correct option is 1.
Question 2
1 / -0

Ratio of volumes of two cones with same radii is

A
h₁: h₂

B
r₁ : r₂

C
s₁ : s₂

D
none of these

Solution

Let Radius and hight of cone (1) is r₁ and h₁
Radius and hight of cone (2) is r₂ and h2
volume of cone (1) =
Volume of cone (2)
ratio =

(because r₁ = r₂)

Volume of the cone (1) : Volume of the cone (2) = h₁ : h₂

Correct option is 1.
Question 3
1 / -0

A right circular cone is given a height of 6 cm and its semi vertical angle is 30°. Find its volume.

A
18

B
24

C
36

D
20

Solution

radius ( r ) =

Volume of the right circular cone =

Correct option is 2.
Question 4
1 / -0

A cylinder of the maximum possible size is made out of a solid wooden cube with each side 20 cm. What percentage of material (approx.) is left in this process?(Take π = 3.14)

A
20%

B
25%

C
22%

D
30%

Solution

Volume of cube (V) = Side³ = 20³ cm³Volume of cylinder (v) =

% of Material left =

= (100 - 78.5) %
= 21.5 % ≈ 22

Hence, 22% is the correct answer.
Question 5
1 / -0

Ratio of volumes of two cones with the same height is

A
r₁: r₂

B
r₁² : r₂²

C
h₁² : h₂²

D
none of these

Solution

Let thr radius and height of cone (1) is r1 and h1
Radius and height of cone (2) is r2 and h2
Volume of cone (1) =
Volume of cone (2) =
Ratio =

( because h₁ and h₂ = h)

Volume of cone (1) : Volume of cone (2) =

Correct option is 2
Question 6
1 / -0

Ratio of curved surface areas of two cylinders with different radii R and r; but equal height is

A
H : h

B
R : r

C
1 : 2

D
none of these

Solution

Curved surface area of cylinder (1) =
Curved surface area of cylinder (2) =
Ratio =

Ratio = R : r

Correct option is 2.
Question 7
1 / -0

Ratio of volumes of two cylinders with equal height is

A
R : r

B
H : h

C
R² : r²

D
none of these

Solution

Let the radius of cylinder (1) = R
Radius of cylinder (2) = rRatio =

Ratio =

Correct option is 3
Question 8
1 / -0

The area of the base of a cone is 1386 sq cm. Its height is 28 cm. Its total surface area is

A
3696 cm²

B
2810 cm²

C
2610 cm²

D
2685 cm²

Solution

Let the radius of the base of a cone = r cm
Area of the base of a cone = 1386 cm²
now,

Slant height ,

Total surface area of a cone =

Correct option is 1.
Question 9
1 / -0

Ramesh cuts a semi-circle of radius 4 cm from a piece of paper and then folds it in such a way that it forms a cone. What is the volume of the cone so formed?

A
(8)/cm³

B
cm³

C
8 cm³

D
cm³

Solution

From the question, slant height of the cone (l) = Radius of the semi-circle (R)
l = 4 cm
Let the radius of the base of the cone be r cm.
Now, circumference of the base of the cone = Circumference of the semi-circle

Slant height,

Therefore, height, h =

Volume of the cone =

The correct option is (1).
Question 10
1 / -0

A circular disc of area 0.49m² rolls down a length of 1.76 km. What is the number of revolutions it makes?

A
300

B
400

C
600

D
4,000

Solution

Let the radius of the circular disc = r m

Area of the circular disc,

(given)

Circumference of the circular disc,

2πr = 2 × × 0.7 = 4.4
Number of revolutions =
Question 11
1 / -0

The ratio of the radius of the base to the height of a cone is 5 : 12. If the cost of smoothening the curved surface area (CSA) is Rs. 115.50 at a rate of 5 paise per sq. cm, then what is the total surface area of the cone?

A
3696.36 cm²

B
3693 cm²

C
3198.46 cm²

D
3332 cm²

Solution

Slant height,

Curved surface area of the cone x Cost per sq. cm (in Rs.) = Total cost of smoothening

= 2310

= 2310

Total surface area of the cone = C.S.A + = 2310 + = = 3198.46 cm²
Question 12
1 / -0

Ratio of curved surface areas of two cylinders with heights H and h respectively and having equal radii is

A
h : H

B
H² : h²

C
H : h

D
None of these

Solution

Let height of the cylinder (A) = H
Height of the cylinder (B) = h
Radius of the cylinder (A) = R
Radius of the cylinder (B) = r
Given that, R = r
Ratio = Curved surface of cylinder (A)/Curved surface cylinder (B)

(Because is constant and R = r)

The correct option is 3.
Question 13
1 / -0

The ratio of volumes of two cylinders with heights H and h respectively and having equal radii (R = r) is

A
R : r

B
H : h

C
R² : r²

D
none of these

Solution

Let the Radius of the cylinder (A) = R
the Height of the cylinder (A) = H
the Radius of the cylinder (B) = r
the height of the cylinder (B) = h

Given that , R = r

Ratio

Correct potion is 2.
Question 14
1 / -0

The cost of painting the curved surface area of cone is Rs. 35.20 at 5 paise per cm². What will be the approximate height of the cone if its slant height is 25 cm?

A
25 cm

B
23 cm

C
34 cm

D
36 cm

Solution

Given slant height of the cone (l) = 25 cm

Curved surface area of the cone = Curved surface area of the cone Cost per cm² = Total cost of painting

3.925r = 35.2

r =

Let height of the cone be 'h'.
Question 15
1 / -0

The radius of the base of a right circular cone is 6 cm and its slant height is 28 cm. The curved surface area of the cone is

A
268 cm²

B
658 cm²

C
462 cm²

D
528 cm²

Solution

Given:
Radius of the right circular cone = 6 cm
Slant height of the right circular cone = 28 cm
Curved surface area of the right circular cone

Hence, option (4) is the correct answer.
Question 16
1 / -0

A copper sphere of diameter 18 cm is melted and converted into a wire of diameter 4 mm. The length of the wire (in metres) is

A
143

B
243

C
343

D
743

Solution

Diameter of the sphere (D) = 18 cm
Radius of the sphere (R)
Diameter of the wire ( d ) = 4 mm = 0.4 cm
Radius of the wire ( r )

According to the question,
Volume of the Sphere = Volume of the wire ( cylinder )

Correct option is 2.
Question 17
1 / -0

A vessel of solid cyllinderical shape, having volume of 33.264 litres is casted into a conical shape. If its height is 72 cm, what is the cost of painting its CSA at Rs. 12 per sq m?

A
Rs.5.94

B
Rs.6.94

C
Rs.7.95

D
None of these

Solution

Volume of the vessel of solid cylinderical shape ( V ) = 33.264 litres = 0.033264 m³
Height of the cone ( h ) = 72 cm = 0.72 m

According to the question,
Volume of the cone = Volume of the vessel of solid cylindrical shape

Slant height,

Curved surface area of the cone (CSA) =

Total cost of painting =

Correct option is 1.
Question 18
1 / -0

The base radius of a cylinder is 2 times its height. The cost of painting its CSA at 4 paise/cm² is Rs. 100. The volume of the cylinder is approximately

A
34464.64 cm³

B
80580 cm³

C
50500 cm³

D
None of these

Solution

Let radius of the cylinder be r.
Let height of the cylinder be h.
Given, r = 2h

Curved surface area of the cylinder Cost per cm² = Total cost of painting

Volume of the cylinder

Coreect option is 1.
Question 19
1 / -0

The lateral surface area of a cylinder is 220 sq. cm with height 7 cm. Its volume is

A
200 cm³

B
212 cm³

C
650 cm³

D
550 cm³

Solution

Given:
Height of the cylinder (h) = 7 cm
Lateral Surface area of cylinder = 220 cm2

Volume of the cylinder (V)

Hence, option (4) is the correct answer.
Question 20
1 / -0

Thirty buckets of lime are used to form a conical heap. Each bucket has a radius of 14 cm and a height of 15 cm. If the base area of the conical heap is 5544 cm², the area of canvas required to cover it is

A
1980 cm²

B
19,800 cm²

C
198 cm²

D
None of these

E
2200 cm²

Solution

Radius of the bucket (R) = 14 cm
Height of the bucket (H) = 15 cm
Area of the base of the cone = πr² = 5544 cm²r = 42 cm
Volume of the bucket (V) = πR²H = 3.14 × 14² × 15 = 9231.6 cm³Volume of the cone = 30 × volume of the bucket

× π × r² × h = 30 × 9231.6

× 3.14 × 42² × h = 2,76,948

h = 150 cm
Slant height, l² = r² + h² = 42² + 150²l² = 1764 + 22,500 = 24,264
l = 155.769 cm
Curved surface area of the cone = πrl = 3.14 × 42 × 155.769 = 20,542.81 cm²Hence, option (4) is correct.