Assertion & Reason Test: Surface Area & Volumes - Class 10 MCQ

# Assertion & Reason Test: Surface Area & Volumes - Class 10 MCQ

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## 15 Questions MCQ Test Mathematics (Maths) Class 10 - Assertion & Reason Test: Surface Area & Volumes

Assertion & Reason Test: Surface Area & Volumes for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Assertion & Reason Test: Surface Area & Volumes questions and answers have been prepared according to the Class 10 exam syllabus.The Assertion & Reason Test: Surface Area & Volumes MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Surface Area & Volumes below.
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Assertion & Reason Test: Surface Area & Volumes - Question 1

### Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The radii of two cone are in the ratio 2 : 3 and their volumes in the ratio 1 : 3. Then ratio of their heights is 3 : 2.Reason (R): Volume of Cone =

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 1
Let V1, V2 are the volumes of the two cones.

R and r be the radii of the two cones.

H and h be the heights of the two cones.

which proves that assertion is wrong.

Therefore, A is false but R is true.

Assertion & Reason Test: Surface Area & Volumes - Question 2

### Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the volume of two spheres are in the ratio 27 : 8. Then their surface area are in the ratio 3 : 2.Reason (R): Volume of sphere = and its surface area = 4πr2.

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 2

Let S1 and S2 be the surface area of two spheres,

which proves that assertion is wrong.

Therefore, A is false but R is true.

Let V1, V2 are the volumes of the two spheres.

R and r be the radii of the two spheres.

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Assertion & Reason Test: Surface Area & Volumes - Question 3

### Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the height of the cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.Reason (R): If r be the radius of the cone and h be the height of the cone, then slant height =

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 3
slant height =

which proves that assertion is wrong.

Therefore, A is false but R is true.

Assertion & Reason Test: Surface Area & Volumes - Question 4

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.

Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 4
Volume of sphere =

Also, S = 4πr2

which proves that assertion is correct.

Therefore, Both A and R are true and R is the correct explanation for A.

Assertion & Reason Test: Surface Area & Volumes - Question 5

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. The volume of the solid is π cm3.

Reason (R): Volume of cone = and volume of hemi-sphere =

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 5
Volume of the Solid =

Which is true.

Therefore, Both A and R are true and R is the correct explanation for A.

Assertion & Reason Test: Surface Area & Volumes - Question 6

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): There are 1000 balls of diameter 0.6 cm which can be formed by melting a solid sphere of radius 3 cm.

Reason (R):Number of spherical balls = (Volume of Bigger solid sphere)/(Volume of 1 spherical ball)

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 6
radius of Ball = 0.3 cm and radius of solid sphere = 3 cm Volume of solid sphere = n × volume of 1 ball here n represents number of balls

Which proves both Assertion and reason are true.

Therefore, Both A and R are true and R is the correct explanation for A.

Assertion & Reason Test: Surface Area & Volumes - Question 7

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): A solid iron is in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere. Then the radius of sphere will be 21 cm.

Reason (R): Volume of cylinder = πr2h, r is the radius of the cylinder and h is the height of the cylinder.

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 7
Let r be the radius of the sphere, Volume of sphere = Volume of the cuboid

⇒ r = 21 cm, which is true.

The reason is also true but it doesn’t explain the assertion as the formula given is of cylinder.

Therefore, Both A and R are true and R is not correct explanation for A.

Assertion & Reason Test: Surface Area & Volumes - Question 8

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): A manufacturer involved children in colouring playing top (Lattu) which is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. The area to be painted if 100 playing tops are given to him then will be 3955 cm2.

Reason (R): Slant height =

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 8
The formula of slant height is wrong.

The correct formula is l =

Therefore, A is true but R is false.

Assertion & Reason Test: Surface Area & Volumes - Question 9

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm2 .

Reason : If r be the radius and h be the height of the cylinder, then total surface area = (2prh +2pr2).

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 9
Total surface area = 2prh +2pr2

= 2p r (h + r)

= 3872 cm2

Assertion & Reason Test: Surface Area & Volumes - Question 10

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.

Reason : If r be the radius and h the slant height of the cone, then slant height =

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 10
Assertion (A) is false but reason (R) is true.

Slant height =

Assertion & Reason Test: Surface Area & Volumes - Question 11

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.

Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 11
As

Assertion & Reason Test: Surface Area & Volumes - Question 12

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : If a ball is in the shape of a sphere has a surface area of 221.76cm2 , then its diameter is 8.4 cm.

Reason : If the radius of the sphere be r , then surface area, S = 4p r2 , i.e.

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 12
Given, surface area of sphere = 221.76cm2

We know, surface area of sphere = 4πr2

⇒ 4(π)r2 = 221.76

⇒ r2 = 7/22​ × 221.76 × 1/4 ​= 7 × (10.08) × 1/4 ​

⇒ r = 4.2cm

Then, diameter equals 2r = 2 × 4.2 = 8.4 cm, which is true and reason is also correct.

Moreover reason is the correct explanation of assertion.

Assertion & Reason Test: Surface Area & Volumes - Question 13

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : No. of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm. in diameter, is 2541

Reason : Number of balls

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 13
n * (volume of small spheres) = total volume

n ∗ (4/3) ∗ (22/7) ∗ 23 = (44)3

n = (3/4) ∗ (7/22) ∗ (1/8) ∗ (44)3 = 2541

As per the given reason, n = (volume of one ball)/(volume of lead)

Thus, reason is not correct but assertion is correct.

Assertion & Reason Test: Surface Area & Volumes - Question 14

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The slant height of the frustum of a cone is 5 cm and the difference between the radii of its two circular ends is 4 cm. Than the height of the frustum is 3 cm.

Reason : Slant height of the frustum of the cone is given by

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 14
We have, l = 5 cm , R - r = 4 cm

16 + h2 = 25

h2 = 25 - 16 = 9

h = 3 cm

Assertion & Reason Test: Surface Area & Volumes - Question 15

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Two identical solid cube of side 5 cm are joined end to end. Then total surface area of the resulting cuboid is 300 cm2 .

Reason : Total surface area of a cuboid is 2(lb + bh + lh)

Detailed Solution for Assertion & Reason Test: Surface Area & Volumes - Question 15
When cubes are joined end to end, it will form a cuboid.

l = 2 x 5 = 10 cm , b = 5 cm

and h = 5 cm

Total surface area = 2(lb + bh + lh)

= 2(10 x 5 + 5 + 5 x 10 x 5)

= 2 x 125 = 250 cm2

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## Mathematics (Maths) Class 10

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