Advertisements
Advertisements
प्रश्न
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
Advertisements
उत्तर
Diameter = 10 cm
Therefore, radius (r) = 5 cm
Height of the cone (h) = 12 cm
Height of the cylinder = 12 cm
∴ `l = sqrt(h^2 + r^2)`
= `sqrt(12^2 + 5^2)`
= `sqrt(144 + 25)`
= `sqrt(169)`
= 13 cm
i. Total surface area of the solid
= `pirl + 2pirh + 2pir^2`
= `pir(l + 2h + 2r)`
= `22/7 xx 5[13 + (2xx12) + (2 xx 5)]`
= `110/7 [13 + 24 + 10]`
= `110/7 xx 47`
= `5170/7`
= 738.57 cm2
ii. Total volume of the solid
= `1/3pir^2h + pir^2h + 2/3pir^3`
= `pir^2 [1/3h + h + 2/3r]`
= `22/7 xx 5 xx 5[1/3 xx 12 + 12 + 2/3 xx 5]`
= `550/7 [4 + 12 + 10/3]`
= `550/7 [16 + 10/3]`
= `550/7 xx 58/3`
= `31900/21`
= 1519.0476 cm3
iii. Total weight of the solid = 1.7 kg
∴ Density = `"Mass"/"Volume"`
= `(1.7 xx 1000)/(1519.0476)` gm/cm3
= `(17 xx 1000 xx 10000)/(10 xx 15190476)` gm/cm3
= 1.119 gm/cm3
`=>` Density = 1.12 gm/cm3
संबंधित प्रश्न
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
Find the radius of a sphere whose surface area is 154 cm2.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
