標題:
F3 Maths Problems
發問:
1) The surface area of a red-hot steel bar decreases by 5% when it completely cools down. Find the percentage change in its length.(Give the answer correct to 2 significant figures.)2) Show that the volume V of a sphere with diameter d and surface area A is given by V=(1/6)Ad.3) Air is leaking out from a... 顯示更多 1) The surface area of a red-hot steel bar decreases by 5% when it completely cools down. Find the percentage change in its length.(Give the answer correct to 2 significant figures.) 2) Show that the volume V of a sphere with diameter d and surface area A is given by V=(1/6)Ad. 3) Air is leaking out from a spherical balloon.Find the percentage decrease in its volume when its volume when its surface area has decreased by 36%. Need Steps, plz!
最佳解答:
1. V : volume of the steel bar L : length of the steel bar V ∝ L3 Hence V = k L3, where k is a non-zero constant. When V = Vo, L = Lo : Vo = k Lo3 Lo = ?(Vo / k) When V = (1 - 5%)Vo : (1 - 5%)Vo = k L3 L = ?(0.95 Vo / k) L = ?(0.95)Lo Percentage change in its length = {[?(0.95)Lo - Lo]/Lo}× 100% = [?(0.95) - 1] × 100% = -1.7% (to 2 sig,. fig.) ==== 2. radius, r = d/2 Area, A = 4 π r2 A = 4 π (d/2)2 A = π d2 Volume, V = (4/3) π r3 V = (4/3) π (d/2)3 V = (4/3) π (d3/8) V = (1/6) π d3 V = (1/6) (π d2) d V = (1/6) A d ==== 3. V : volume of the sphere A : surface area of the sphere r : radius of the sphere A ∝ r2 ..and.. V ∝ r3 A3 ∝ r? ..and.. V2 ∝ r? Hence, V2 ∝ A3 V2 = k A3,where k is a non-zero constat When V = Vo, A = Ao : Vo2 = k Ao3 Vo = √{k Ao3} When A = (1 - 36%)Ao : V = √{k [(1 - 0.36%)Ao]3} V = √{k [0.64Ao]3} V = (√0.643) √{k Ao3} V = 0.512 Vo Percentage decrease in volume = [(Vo - 0.512 Vo) / Vo] × 100% = 48.8%
其他解答:
F3 Maths Problems
發問:
1) The surface area of a red-hot steel bar decreases by 5% when it completely cools down. Find the percentage change in its length.(Give the answer correct to 2 significant figures.)2) Show that the volume V of a sphere with diameter d and surface area A is given by V=(1/6)Ad.3) Air is leaking out from a... 顯示更多 1) The surface area of a red-hot steel bar decreases by 5% when it completely cools down. Find the percentage change in its length.(Give the answer correct to 2 significant figures.) 2) Show that the volume V of a sphere with diameter d and surface area A is given by V=(1/6)Ad. 3) Air is leaking out from a spherical balloon.Find the percentage decrease in its volume when its volume when its surface area has decreased by 36%. Need Steps, plz!
最佳解答:
1. V : volume of the steel bar L : length of the steel bar V ∝ L3 Hence V = k L3, where k is a non-zero constant. When V = Vo, L = Lo : Vo = k Lo3 Lo = ?(Vo / k) When V = (1 - 5%)Vo : (1 - 5%)Vo = k L3 L = ?(0.95 Vo / k) L = ?(0.95)Lo Percentage change in its length = {[?(0.95)Lo - Lo]/Lo}× 100% = [?(0.95) - 1] × 100% = -1.7% (to 2 sig,. fig.) ==== 2. radius, r = d/2 Area, A = 4 π r2 A = 4 π (d/2)2 A = π d2 Volume, V = (4/3) π r3 V = (4/3) π (d/2)3 V = (4/3) π (d3/8) V = (1/6) π d3 V = (1/6) (π d2) d V = (1/6) A d ==== 3. V : volume of the sphere A : surface area of the sphere r : radius of the sphere A ∝ r2 ..and.. V ∝ r3 A3 ∝ r? ..and.. V2 ∝ r? Hence, V2 ∝ A3 V2 = k A3,where k is a non-zero constat When V = Vo, A = Ao : Vo2 = k Ao3 Vo = √{k Ao3} When A = (1 - 36%)Ao : V = √{k [(1 - 0.36%)Ao]3} V = √{k [0.64Ao]3} V = (√0.643) √{k Ao3} V = 0.512 Vo Percentage decrease in volume = [(Vo - 0.512 Vo) / Vo] × 100% = 48.8%
其他解答:
此文章來自奇摩知識+如有不便請留言告知
文章標籤
全站熱搜
留言列表
