Conversion Of Solid From One Shape To Another
Solid is a three dimensional definite shape. Cuboid, cone, cylinder, and sphere are the some of the examples of solids. Conversion of Solid from One Shape to another involves changing the shape of an object into another object for some particular issue. When we convert the solid from one shape into another the volume of the shape is preserved but the surface area will change usually.
Conversion of Solid from One Shape to another - Picture:
The below diagram shows the Conversion of Solid from One Shape to another . Converting the cube into small spheres by cutting the cube.
cube to sphere
Example Problems on Conversion of Solid from One Shape to another :
Ex 1:
A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of pop-corn. The pop-corn is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with pop-corn.
Sol:
Step 1: Finding the volume of cylinder
Diameter of the cylinder = d= 24 cm ,
Radius = r = d/2 = 12 cm
Height = h= 10 cm
Formula to find the Volume of cylinder = 'pi' r2 h
= 'pi' 12 x12x10
=1440 'pi' cubic centimeter
Step 2: Finding volume of cone
Height of the cone = 8 cm, radius = 4/2 = 2cm
Volume of one pop-corn cone including top = 1/3 'pi' r2 h + 2/3 'pi' r3
=( 1/3 'pi'2x2 x8 )+ ( 2/3 x pi x 2x2x2)
= 10.66'pi'
= 15.99 'pi'
Step 3: Finding number of cones
No. of cones = Volume of cylinder/ volume of one cone with top
= '(1440pi) / (16 pi)'
= 90
Hence 90 cones can be filled with popcorn in the container.
Ex 2:
A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24cm and the total height of the container is 16 cm. Find its capacity.
Sol:
Diameter of the container =d = 24 cm
Radius of the hemispherical container = r = 12 cm
Radius of the cylinder = Radius of the hemisphere = 12cm
Height of the cylinder = height of the container "" radius of the hemisphere
= 16- 12
= 4cm
Capacity of the container = volume of the hemisphere + volume of the cylinder.
= 2/3 'pi' r3+ 'pi' r2 h
= (2/3 x 3.14 x 123) + (3.14 x 122 x 4)
= 3617.28 + 1808.64
= 808.64 cu. cm
Hence the capacity of container = 808.64 cu. cm
The base, is the number of digits in a number system. The base number that is going to raise a power (i.e. 1012 "" here 2 is base number of 101). In other words we can say that radix of 2.We have several base number systems like binary, decimal, octal and hexadecimal. Base number conversion systems are generally used in arithmetic, computing and different kinds of purposes.
Different Kinds of Base Number Conversions
Where we are using this base number conversion system?
Especially base 10 (decimal number system) is used in arithmetic operations; the numbers are 0 to 9. Base 2 (binary number system, the number are 0 and 1), base 8 (the number are 0 to 7) and base 16 (the digits are "0 to 9" followed by "A to F") number system are used in computing. Remaining numbers are used in different kinds of criteria.
How do we convert a number from another base into base?
Base number conversion example 1:
Convert 1012 to decimal number system (base 10).
1012 = (1 * 20 + 0 * 21 + 1 * 22)10
= (1 * 1 + 0 * 2 + 1 * 4)10
= (1 + 0 + 4)10
1012 = 510
Whether is it right? We can check the problem via reverse conversion like base 10 to base 2.
Step1: Divide 5 by 2, quotient is 2, remainder is 1.
Step2: Divide quotient 2 by 2, quotient is 1 remainder 0.
Write the final quotient value first then take all remainder from bottom to top. Then we can write as,
510 = 1012
Shall we discuss about more examples in the base number system.
Base number conversion example 2:
Convert 11012 to base 8
11012 = (1 * 20 + 1 * 21 + 0 * 22 + 1 * 23 )8
= (1 * 1 + 1 * 2 + 0 * 4 + 1 * 8)8
= (1 + 2 + 0 + 8)8
= 118
Verification
Step1: Divide 11 by 2, quotient is 5, remainder is 1.
Step2: Divide quotient 5 by 2, quotient is 2, remainder 1.
Step3: Divide quotient 2 by 2, quotient is 1, remainder 1.
118 = 11112
Exercise on Base Number Conversion
Problems:
Convert 1112 to base 10.
Convert 88 to base 2.
Convert 1AF16 to base 10.
Convert 3118 to base 10.
Answer key:
7
1000
43110
20110
Conversion of Solid from One Shape to another - Picture:
The below diagram shows the Conversion of Solid from One Shape to another . Converting the cube into small spheres by cutting the cube.
cube to sphere
Example Problems on Conversion of Solid from One Shape to another :
Ex 1:
A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of pop-corn. The pop-corn is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with pop-corn.
Sol:
Step 1: Finding the volume of cylinder
Diameter of the cylinder = d= 24 cm ,
Radius = r = d/2 = 12 cm
Height = h= 10 cm
Formula to find the Volume of cylinder = 'pi' r2 h
= 'pi' 12 x12x10
=1440 'pi' cubic centimeter
Step 2: Finding volume of cone
Height of the cone = 8 cm, radius = 4/2 = 2cm
Volume of one pop-corn cone including top = 1/3 'pi' r2 h + 2/3 'pi' r3
=( 1/3 'pi'2x2 x8 )+ ( 2/3 x pi x 2x2x2)
= 10.66'pi'
= 15.99 'pi'
Step 3: Finding number of cones
No. of cones = Volume of cylinder/ volume of one cone with top
= '(1440pi) / (16 pi)'
= 90
Hence 90 cones can be filled with popcorn in the container.
Ex 2:
A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24cm and the total height of the container is 16 cm. Find its capacity.
Sol:
Diameter of the container =d = 24 cm
Radius of the hemispherical container = r = 12 cm
Radius of the cylinder = Radius of the hemisphere = 12cm
Height of the cylinder = height of the container "" radius of the hemisphere
= 16- 12
= 4cm
Capacity of the container = volume of the hemisphere + volume of the cylinder.
= 2/3 'pi' r3+ 'pi' r2 h
= (2/3 x 3.14 x 123) + (3.14 x 122 x 4)
= 3617.28 + 1808.64
= 808.64 cu. cm
Hence the capacity of container = 808.64 cu. cm
The base, is the number of digits in a number system. The base number that is going to raise a power (i.e. 1012 "" here 2 is base number of 101). In other words we can say that radix of 2.We have several base number systems like binary, decimal, octal and hexadecimal. Base number conversion systems are generally used in arithmetic, computing and different kinds of purposes.
Different Kinds of Base Number Conversions
Where we are using this base number conversion system?
Especially base 10 (decimal number system) is used in arithmetic operations; the numbers are 0 to 9. Base 2 (binary number system, the number are 0 and 1), base 8 (the number are 0 to 7) and base 16 (the digits are "0 to 9" followed by "A to F") number system are used in computing. Remaining numbers are used in different kinds of criteria.
How do we convert a number from another base into base?
Base number conversion example 1:
Convert 1012 to decimal number system (base 10).
1012 = (1 * 20 + 0 * 21 + 1 * 22)10
= (1 * 1 + 0 * 2 + 1 * 4)10
= (1 + 0 + 4)10
1012 = 510
Whether is it right? We can check the problem via reverse conversion like base 10 to base 2.
Step1: Divide 5 by 2, quotient is 2, remainder is 1.
Step2: Divide quotient 2 by 2, quotient is 1 remainder 0.
Write the final quotient value first then take all remainder from bottom to top. Then we can write as,
510 = 1012
Shall we discuss about more examples in the base number system.
Base number conversion example 2:
Convert 11012 to base 8
11012 = (1 * 20 + 1 * 21 + 0 * 22 + 1 * 23 )8
= (1 * 1 + 1 * 2 + 0 * 4 + 1 * 8)8
= (1 + 2 + 0 + 8)8
= 118
Verification
Step1: Divide 11 by 2, quotient is 5, remainder is 1.
Step2: Divide quotient 5 by 2, quotient is 2, remainder 1.
Step3: Divide quotient 2 by 2, quotient is 1, remainder 1.
118 = 11112
Exercise on Base Number Conversion
Problems:
Convert 1112 to base 10.
Convert 88 to base 2.
Convert 1AF16 to base 10.
Convert 3118 to base 10.
Answer key:
7
1000
43110
20110
