Match the following.
Column –I | Column –II |
(i) Circular plate is expanded by heat from radius 5 cm to 5.06 cm. The approximate increase in area is | [A] 4 |
(ii) Sides of a cube increasing by 1% then the percentage increase in volume is | [B] 0.6π |
(iii) If the rate of decrease of – 2x + 5 is twice the rate of decrease of x, then x is equal to | [C] 3 |
(iv) Rate of increase in area of equilateral triangle of side 15 cm, when each side is increasing at the rate of 0.1 cm/s is | [D] |
Text Solution
Verified by Experts(i) [B]; (ii) [C]; (iii) [A]; (iv) [D]
Ans.
(i) [B]
(ii) [C]
(iii) [A]
(iv) [D]
Sol.
Given, r = 5 cm, δ r = 0.06
∴ A = π r 2 ⇒ δ A = 2 π r δ r = 10 π × 0.06 = 0.6 π .
Let V = x
3 ⇒ δ V = 3x 2 δ x
∴ 
× 100 = 
× 100 = 3 × 1 = 3
Since, (x – 2) 
= 
⇒ x = 4.
A = 
= 
= 
= 
cm 2 /s.
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