The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.
Given length of cuboid , l = 44 cmBreadth of cuboid ,b = 21 cmHeight of cuboid , h = 12cmVolume of the cuboid , V = lbhV = 44×21×12 = 11088cm3Given Height of cone ,h = 24cmSince cuboid is melted and a cone is made, the volume will be same.Volume of cone = Volume of cuboid.(1/3)r2h = […]
Find the surface area of a sphere of radius 7 cm.
Given radius of sphere , r = 7cmSurface area, A = 4r2A = 4×(22/7)×72= 616 cm2Hence surface area of sphere is 616cm2.
Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.
Given radius of cylinder , r = 5cmHeight of cylinder, h = 40cmTotal surface area of cylinder = 2r(r+h)= 2×(22/7)×5×(5+40)= 2×(22/7)×5×45= 1414.28cm2Hence Total surface area of cylinder is 1414.28cm2.
Find the volume of a sphere of diameter 6 cm.
Given diameter of sphere , d = 6cmRadius r = d/2 = 3Volume of a sphere, V = (4/3)r3V = (4/3)×(22/7)×33V = 113.14cm3Hence the volume of the sphere is 113.14cm3.
Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.
Given radius of cone ,r = 1.5cmHeight of cone ,h = 5cmVolume of the cone , V = (1/3)r2hV = (1/3)×(22/7) ×1.52×5V = 11.785 cm3= 11.79 cm3Hence the volume of the cone is 11.79 cm3.
Prove the following.
(1) sec(1 – sin) (sec + tan) = (sec-secsin)(sec + tan)= (sec-tan)(sec+tan) [secsin = sin/cos = tan]= sec2-tan2= 1 [1+tan2 = sec2]Hence proved. (2) (sec + tan) (1 – sin) = [(1/cos)+(sin/cos)](1 – sin)= [(1+sin)/cos]×(1-sin)= (1-sin2)/cos= cos2/cos= cosHence proved. (3) sec2 + cosec2 = (1/cos2) +(1/sin2)= (sin2+cos2)/sin2 cos2= 1/ sin2 cos2 [sin2+cos2 = 1]= sec2× cosec2Hence proved. (4) cot2 – tan2 = (cosec2-1)-(sec2-1) [∵cot2 = […]
If sec = 13/12 , find the values of other trigonometric ratios
Given sec = 13/12cos = 1/sec = 12/13We have 1+tan2 = sec21+ tan2 = (13/12)2tan2 = (13/12)2-1 = (169/144)-1 = (169-144)/144 = 25/144Taking square root on both sidestan = 5/12cot = 1/tan = 12/5sin/cos = tansin = tan×cossin = (5/12)×(12/13)sin = 5/13cosec = 1/sin = 13/5Hence cos = 12/13 , tan = 5/12, cot = 12/5 , sin […]
If tan = 2, find the values of other trigonometric ratios.
Given tan = 2We have 1+tan2 = sec21+22 = sec2sec2 = 5Taking square root on both sidessec =√5cos = 1/sec = 1/√5tan = sin/cos2 = sin÷(1/√5)sin = 2/√5cosec = 1/sincoesc = √5/2cot= 1/tancot = 1/2Hence sin = 2/√5, cosec = √5/2, cos = 1/√5, sec = √5 and cot = 1/2
If sin = 11/61, find the values of cos using trigonometric identity.
Given sin = 11/61Sin2+cos2 = 1 [Trigonometric identity](11/61)2+cos2 = 1cos2 = 1-(11/61)2= 1-121/3721= (3721-121)/3721= 3600/3721Taking square root on both sidescos = 60/61Hence the value of cos = 60/61.
Choose the correct alternative answer for the following questions.
(1) sin cosec = ?(A) 1 (B) 0 (C) 1/2 (D) √2 Solution:sin = 1/cosecsin cosec =(1/cosec)×cosec = 1Hence option A is the answer. (2) cosec45° =?(A) 1/√2 (B) √2 (C) √3/2 (D) 2/√3 Solution:cosec45 = √2Hence option B is the answer. (3) 1 + tan2 = ?(A) cot2 (B) cosec2 (C) sec2 (D) tan2 Solution:1 + tan2 = sec2Hence […]