As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water.
Given diameter of cylindrical glass , d = 14cmRadius , R = 14/2 = 7cmHeight of glass in cylindrical glass, H = 30cmGiven diameter of metal sphere = 2cmradius of metal sphere , r = 2/2 = 1cmVolume of sphere = (4/3)r3= (4/3)××13= (4/3)= (4/3)×(22/7)= 4.19cm3Volume of water with sphere in it = R2H= ×72×30= […]
Find the surface area and the volume of a beach ball shown in the figure.
Given diameter of ball , d = 42 cmradius of ball , r = 42/2 = 21cmSurface area of sphere = 4r2= 4××212 = 4×3.14×441 = 5538.96 cm2Volume of sphere = (4/3)r3= (4/3)××213 = (4/3)×3.14×9261 = 38772.72 cm3Hence the surface area and volume of ball are 5538.96 cm2 and 38772.72 cm3 respectively.
Figure 7.13 shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and the surface area of the toy from the measures shown in the figure.(=3.14)
Given radius of cone ,r = 3 cmHeight of cone ,h = 4 cmRadius of hemisphere, r = 3cmSlant height of cone , l = √(h2+r2)l = √(42+32) = √(16+9) = √25 = 5Curved surface area of cone = rl= ×3×5 = 15cm2Curved surface area of hemisphere = (2/3)r3= (2/3)×33 = 18cm2Surface area of toy = Curved surface area […]
In the figure 7.12, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. How many such tablets are wrapped in the wrapper ?
Given radius of tablet, r = 7mmThickness of tablet , h = 5mmVolume of tablet =Radius of cylindrical wrapper , R = 14/2 = 7mmHeight of cylindrical wrapper , H = 10cm = 10×0 = 100mmLet n be the number of tablets that can be wrapped.n = volume of cylindrical wrapper/volume of tablet= R2H/r2h=× 72×100/×72×5= […]
A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm2 .The cone is placed upon the cylinder. Volume of the solid figure so formed is 500 cm3 . Find the total height of the figure.
Given height of cylinder , h = 3cmBase area of cylinder , r2 = 100cm2 …………..(i)Volume of solid = 500cm3Given cylinder and cone have equal bases. the radii will be equal.Radius of cone = radius of cylinder = r Let height of cone be HVolume of solid = volume of cylinder + volume of cone500 = r2h+(1/3) […]
Observe the measures of pots in figure 7.8 and 7.9. How many jugs of water can the cylindrical pot hold ?
Given radius of jug , r = 3.5 cmHeight of jug , h = 10 cmVolume of conical jug, V = (1/3)r2h= (1/3)××3.52×10 = (122.5/3)×Given Radius of pot ,R = 7cmHeight of pot, H = 10 cmVolume of pot = R2H= ×72×10 = 490Number of jugs of water the cylindrical pot can hold = Volume […]
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.