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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता ९ वी

If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )

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प्रश्न

If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )

बेरीज
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उत्तर

Radius of the hemisphere, r = 5 cm

∴ Curved surface area of the hemisphere = 2πr

= 2 × 3.14 × (5)2 

= 157 cm2

Total surface area of the hemisphere = 3πr

= 3 × 3.14 × (5)2 

= 235.5 cm2

Thus, the curved surface area and total surface area of the solid hemisphere is 157 cm2 and 235.5 cm2, respectively.

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पाठ 9: Surface Area and Volume - Practice Set 9.3 [पृष्ठ १२३]

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बालभारती Mathematics 2 [English] Standard 9 Maharashtra State Board
पाठ 9 Surface Area and Volume
Practice Set 9.3 | Q 2. | पृष्ठ १२३

संबंधित प्रश्‍न

Find the surface area of a sphere of diameter 14 cm.

`["Assume "pi=22/7]`


Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]


The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.


A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

`["Assume "pi = 22/7]`


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.


A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.


Find the surface area of a sphere of radius 10.5 cm. 


Find the surface area of a sphere of radius 14 cm.


Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)


A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.


The volume of a sphere is 38808 cm3; find its diameter and the surface area.


Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere. 


A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast. 


Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm. 


A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.


A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.


A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl. 


A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid. 


The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire. 


Find the total surface area of a hemisphere of radius 10 cm.


How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?


If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.


If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is 


If the surface area of a sphere is 144π m2, then its volume (in m3) is 


A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes 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 and volume of sphere of the following radius.  (π = 3.14 )

3.5 cm


If the surface area of a sphere is 2826 cmthen find its volume. ( π= 3.14)


Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m. 


A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere . 


A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder . 


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 :

  1. the total surface area.
  2. the total volume of the solid and
  3. the density of the material if its total weight is 1.7 kg.

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 used.


There is surface area and volume of a sphere equal, find the radius of sphere.


The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.


A solid sphere is cut into two identical hemispheres.

Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid?


A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm3 of ball bearings. Find the:

  1. maximum number of ball bearings that each box can have.
  2. mass of each box of ball bearings in kg.
    (Use π = `22/7`)

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