 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says the diameter of a sphere is decreased by 25% by what person does its curved surface area decrease. So let us start with the solution to this question. First of all let D be the diameter of the sphere, its surface area will be equal to into D by 2 the whole square because we see that if D is the diameter then D by 2 will be the radius and the formula for surface area of a sphere is 4 into pi into square of the radius. So radius in this case is D by 2 that is equal to because here in the denominator we will have 2 square that is 4 so 4 would get cancelled with 4 we have pi D square. Now increasing its diameter percent the new diameter will be and that means now only 75% of the diameter D is left so D1 will be 75% of D by 4 because we see that when we cancel 75 by 100 we get 3 by 4. So now new diameter is 3D by 4 therefore we will have a new surface area will be equal to into pi into the new radius 4 the whole square pi into 9D square divided by 2A that is 64. Now this will be equal to we know that D square minus D square minus pi D square into 9 by 16 that is equal to pi D square into 1 minus 9 by 16 and that is equal to 7 by 16. Therefore initial surface area into 100% see that decrease in surface area is pi D square into 7 by 16 so it is pi D square into 7 by 16 into 1 upon initial surface area was gets cancelled by pi D square and we have 100 by 6 by 43.75 per area decreases. So this is our question and enjoyed the session have a good day.