Q. 795.0( 1 Vote )
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
Assertion (A): If the volumes of two sphere are in the ratio 27:8 then their surface areas are in the ratio 3:2
Reason (R): Volume of a sphere 
.
Surface area of a sphere = 4πR2.
A. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
B. Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
C. Assertion (A) is true and Reason (R) is false.
D. Assertion (A) is false and Reason (R) is true.
Answer :
Assertion is wrong and Reason is Wrong.
Explanation:
Assertion (A):
Given: volumes of two sphere are in the ratio 27:8.
Volume of the sphere is given by: 
πr3
Let V1 be the volume of the first sphere.
Let V2 be the volume of the first sphere.
∴ V1:V2 = 
π(r1)3 : 
π(r2)3
⇒ 27:8 = (r1)3 : (r2)3
⇒ r1 : r2 = 3:2
Surface area of the sphere is given by: 4πr2
Let S1 be the Surface area of the sphere.
Let S2 be the Surface area of the sphere.
∴ S1 : S2 = 4π(r1)2:4π(r2)2
⇒ S1 : S2 = (r1)2: (r2)2
⇒S1 : S2 = (3)2: (2)2
⇒S1 : S2 = 9:4
Reason(R):
Volume of a sphere = 
πr3.
Surface area of a sphere = 4πR2.
Assertion is wrong and Reason is Wrong.
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PREVIOUSEach question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:Assertion (A): The number of coins 1.75 cm in diameter and 2 mm thick from a melted cuboid (10 cm × 5.5 cm × 3.5 cm) is 400.Reason (R): Volume of a cylinder of base radius r and height h is given by V= (πr2h) cubic units. And, area of a cuboid = (l × b × h) cubic units.NEXTEach question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:Assertion (A): The curved surface area of a cone of base radius 3 cm and height 4 cm is (15π) cm2.Reason (R): Volume of a cone = πr2h.
