Try yourself: 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 =
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: D
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.
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Q2:
MULTIPLE CHOICE QUESTION
Try yourself: 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.
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: D
⇒
⇒
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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Q3:
MULTIPLE CHOICE QUESTION
Try yourself: 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 =
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: D
slant height =
which proves that assertion is wrong.
Therefore, A is false but R is true.
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Q4:
MULTIPLE CHOICE QUESTION
Try yourself: 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.
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: A
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.
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Q5:
MULTIPLE CHOICE QUESTION
Try yourself: 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 =
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: A
Volume of the Solid =
Which is true.
Therefore, Both A and R are true and R is the correct explanation for A.
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Q6:
MULTIPLE CHOICE QUESTION
Try yourself: 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)
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: A
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.
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Q7:
MULTIPLE CHOICE QUESTION
Try yourself: 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.
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: B
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.
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Q8:
MULTIPLE CHOICE QUESTION
Try yourself: 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 =
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true and R is not correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
Correct Answer: C
The formula of slant height is wrong.
The correct formula is l =
Therefore, A is true but R is false.
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Q9:
MULTIPLE CHOICE QUESTION
Try yourself: 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).
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C
Assertion (A) is true but reason (R) is false.
D
Assertion (A) is false but reason (R) is true.
Correct Answer: A
Total surface area = 2prh +2pr2
= 2p r (h + r)
= 3872 cm2
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Q10:
MULTIPLE CHOICE QUESTION
Try yourself: 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 =
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C
Assertion (A) is true but reason (R) is false.
D
Assertion (A) is false but reason (R) is true.
Correct Answer: D
Assertion (A) is false but reason (R) is true.
Slant height =
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Q11:
MULTIPLE CHOICE QUESTION
Try yourself: 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.
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C
Assertion (A) is true but reason (R) is false.
D
Assertion (A) is false but reason (R) is true.
Correct Answer: D
As
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Q12:
MULTIPLE CHOICE QUESTION
Try yourself: 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.
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
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.
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Q13:
MULTIPLE CHOICE QUESTION
Try yourself: 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
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C
Assertion (A) is true but reason (R) is false.
D
Assertion (A) is false but reason (R) is true.
Correct Answer: C
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.
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Q14:
MULTIPLE CHOICE QUESTION
Try yourself: 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
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C
Assertion (A) is true but reason (R) is false.
D
Assertion (A) is false but reason (R) is true.
Correct Answer: A
We have, l = 5 cm , R - r = 4 cm
16 + h2 = 25
h2 = 25 - 16 = 9
h = 3 cm
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Q15:
MULTIPLE CHOICE QUESTION
Try yourself: 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)
A
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C
Assertion (A) is true but reason (R) is false.
D
Assertion (A) is false but reason (R) is true.
Correct Answer: D
When cubes are joined end to end, it will form a cuboid.
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which proves that assertion is wrong.
and its surface area = 4πr2.
which proves that assertion is correct.
and volume of hemi-sphere = 
