The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?
Harshit Singh , 4 Years ago
Grade 12th pass
9 grade maths> The diameter of a sphere is decreased by ...
2 AnswersPawan Prajapati
Last Activity: 4 Years ago
. Let diameter of the sphere = d units. Radius = d . - umts. 2 Surface area = 4x(:J sq. units = rril2 sq. units. ..•(i) Diameter of new sphere = (d -t;! d ) units = d units. Radius of new sphere = 8d units. .. Surface area of new sphere = 41t(idJ = 9 n_a_i-2 sq. um•ts. ...(i'i') 16 Decrease = (M2 - :aM2 ) sq. units = 7 d 2 rrd2 sq. units. -1t 700 .. Percentage decrease = 16 x 100 = -% 1t d2 16 = 43.75%.
Dhruv Tyagi
Last Activity: 2 Years ago
Given: diameter of a sphere is decreased by 25%.
We have to find the percentage by which its Curved Surface Area decreases.
Let the radius of the sphere be r.
Then its diameter is 2r.
The Surface area of a sphere = 4πr2
The Curved surface area of the sphere = 4πr2
Now it is given in the question that the diameter of the sphere is decreased by 25% hence a new sphere is formed.
Therefore, the diameter of the new sphere can be written as:
= 2r - (25%) of (2r)
= 2r - (25/100) × (2r)
= 2r - (r/2)
= 3r/2
Radius of the new sphere = 1/2 × 3r/2 = 3r/4
Hence, curved surface area of the new sphere = 4π (3r/4)2
= 4π (9r2/16)
= (9πr2)/4
Now, decrease in the original curved surface area = 4πr - (9πr2)/4
= (16πr2- 9πr2)/4
= (7πr2)/4
So, the percentage decrease in the curved surface area is,
= [(7πr2)/4 × 1/(4πr2)] × 100%
= [7/16] × 100%
= 43.75%
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on 9 grade maths
In the figure (not to scale) AB = CD, angle DAP = angle DPA and A,B,C,D are concycli. If angle ADC = 80°, then find angle ACD.
9 grade maths
1 Answer Available
Last Activity: 2 Years ago
What length of tarpaulin 3m wide will be required to make conical tent of height 8m and base radius 6m ? Assume that the extra length of material that will be required for stitching and wastage in cutting is approximately 20cm ( Use pi= 3.14)
9 grade maths
1 Answer Available
Last Activity: 2 Years ago