30..answer no 1 do like example 6 solution TUTORIAL 30The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate ofchange in the area and the perimeter of the semicircle when the radius is 5 cm2 A stone dropped into a still pond sends out a circular ripple whose area increases at arate of 5 cm'/s. How fast is the radius of the ripple changing when the radius is 2 cm ?3 Oil from a leaking oil tanker radiates outward in the form of a circular film on the surfaceof the water. If the area of the circle increases at the rate of 400 m'/min, how fast is theradius of the circle increasing when the area is 1225n m.4. The radius, rcm of a circle at time t is given by r = 21 + 3. Determine the rate ofchange in the area when t = 1. (Give your answer in terms of n).5. The area of a semicircle is increasing at the rate of 4n cm s'.Calculate the rate of change in the radius of the semicircle when the radius is 5 cm.6. Oil spilled from a ruptured tanker spreads in a circle whose radius inreases at aconstant rate of 2 cm/s. How fast is the area of the spill increasing after 5 minutes ?1. A closed cuboid has a square base and its height is twice its base. If x is the length ofthe base and x increases at a rate of 3 cm s, find the rate of change of thesurface area when x is 4 cm.8. At what rate is the volume and surface area of a cube is changing when the side is 15cm and each side is increasing at the rate of 0.6 cm/sec.9. The radius of a spherical balloon increases at a rate of 0.2 cms.How fast is the volume changing at a certain instant when its volume is 288t cm.10. A spherical balloon is to be deflated at a rate of p cm's'. The radius of the balloondecreases ata rate of 0.5 cms when its volume is 288t cm.Find the value of p.11. A boy is blowing a spherical balloon at a rate of 50 cm/s. At what rate is the radius ofthe balloon changing when the radius is 10 cm.12. The surface area of a sphere decreases at a rate of 5 m's. How fast is the radiuschanging when the radius is 3 m.13. If the radius of a sphere is increasing at the constant rate of 2 mm per sec, how fast isthe volume changing when the surface area is 8 mm ?4.(Hint: Vaphiere = r: Agphere = 4nr")Answers:dA4( 2)de40 Example 6:A cuboid metal slab has a width of x m, length 2x m and height 2 m.2 m2x mWhen heated, the widih expanded at the rate of 0.01 mh.Find the rate of change of the surface area when the volume is 36 m,Solution:dAdx= 0.01.dt= ?, V = 36dtV =4x4x =36x =2 ( 2x + 4x + 2x)4x + 12xA%3DdAdxdA%3Ddtdtdx0.01 x (8x + 12)%3!0.01 x (8(3) + 12)0.36 m2 h%3DAlternative Solution:A =4x + 12xdAdtdxdx+ 12dt8x%3Ddt8(3)(0.01) + 12 (0.01)0.36 m h

Question

30..answer no 1 do like example 6 solution TUTORIAL 30The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate ofchange in the area and the perimeter of the semicircle when the radius is 5 cm2 A stone dropped into a still pond sends out a circular ripple whose area increases at arate of 5 cm'/s. How fast is the radius of the ripple changing when the radius is 2 cm ?3 Oil from a leaking oil tanker radiates outward in the form of a circular film on the surfaceof the water. If the area of the circle increases at the rate of 400 m'/min, how fast is theradius of the circle increasing when the area is 1225n m.4. The radius, rcm of a circle at time t is given by r = 21 + 3. Determine the rate ofchange in the area when t = 1. (Give your answer in terms of n).5. The area of a semicircle is increasing at the rate of 4n cm s'.Calculate the rate of change in the radius of the semicircle when the radius is 5 cm.6. Oil spilled from a ruptured tanker spreads in a circle whose radius inreases at aconstant rate of 2 cm/s. How fast is the area of the spill increasing after 5 minutes ?1. A closed cuboid has a square base and its height is twice its base. If x is the length ofthe base and x increases at a rate of 3 cm s, find the rate of change of thesurface area when x is 4 cm.8. At what rate is the volume and surface area of a cube is changing when the side is 15cm and each side is increasing at the rate of 0.6 cm/sec.9. The radius of a spherical balloon increases at a rate of 0.2 cms.How fast is the volume changing at a certain instant when its volume is 288t cm.10. A spherical balloon is to be deflated at a rate of p cm's'. The radius of the balloondecreases ata rate of 0.5 cms when its volume is 288t cm.Find the value of p.11. A boy is blowing a spherical balloon at a rate of 50 cm/s. At what rate is the radius ofthe balloon changing when the radius is 10 cm.12. The surface area of a sphere decreases at a rate of 5 m's. How fast is the radiuschanging when the radius is 3 m.13. If the radius of a sphere is increasing at the constant rate of 2 mm per sec, how fast isthe volume changing when the surface area is 8 mm ?4.(Hint: Vaphiere = r: Agphere = 4nr&#34;)Answers:dA4( 2)de40 Example 6:A cuboid metal slab has a width of x m, length 2x m and height 2 m.2 m2x mWhen heated, the widih expanded at the rate of 0.01 mh.Find the rate of change of the surface area when the volume is 36 m,Solution:dAdx= 0.01.dt= ?, V = 36dtV =4x4x =36x =2 ( 2x + 4x + 2x)4x + 12xA%3DdAdxdA%3Ddtdtdx0.01 x (8x + 12)%3!0.01 x (8(3) + 12)0.36 m2 h%3DAlternative Solution:A =4x + 12xdAdtdxdx+ 12dt8x%3Ddt8(3)(0.01) + 12 (0.01)0.36 m h

Accepted Answer

Given: 1) drdt=0.8 cm/s
To find: Rate of change of perimeter and area of semicircle when the radius…

/ The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate of change in the area and the perimeter of the semicircle when the radius is 5 cm