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The height of a cone is 30 cm. A small cone is cut-off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?
Most Upvoted Answer
The height of a cone is 30 cm. A small cone is cut-off at the top by a...
Let the height and radius of original(big) cone be H and R
Let the height and radius of cut off (small) cone be h and r
from similar triangles, we know
H / R = h / r
h = H r / R
since H = 30
h = 30 (r /R) --------(1)
Volume of big cone, V = (1/3) π (R²) H
volume of small cone,v = (1/3) π (r^2) h
V / v = (R²) H / (r²) h = 27 (since volume of small cone is 1/27 of big cone)
(R²) H = 27(r²) h
30 (R²) = 27(r²)h
h = 30(R²) / 27 (r²)
h = (30 /27)(R /r)²---------(2)
equating (1) and (2)
30 (r /R) = (30 /27) (R/r)^2
(r /R)³= 1 / 27
r / R = 1/3
substituting this in (1) h = 30 (r /R)
h = 30 (1/3) = 10 cm
The section is made 20 cm (30 -10) above the base.
Let the height and radius of cut off (small) cone be h and r
from similar triangles, we know
H / R = h / r
h = H r / R
since H = 30
h = 30 (r /R) --------(1)
Volume of big cone, V = (1/3) π (R²) H
volume of small cone,v = (1/3) π (r^2) h
V / v = (R²) H / (r²) h = 27 (since volume of small cone is 1/27 of big cone)
(R²) H = 27(r²) h
30 (R²) = 27(r²)h
h = 30(R²) / 27 (r²)
h = (30 /27)(R /r)²---------(2)
equating (1) and (2)
30 (r /R) = (30 /27) (R/r)^2
(r /R)³= 1 / 27
r / R = 1/3
substituting this in (1) h = 30 (r /R)
h = 30 (1/3) = 10 cm
The section is made 20 cm (30 -10) above the base.
Community Answer
The height of a cone is 30 cm. A small cone is cut-off at the top by a...
H/R=h/r
h=Hr/R
h=30r/R
.................(equation 1)
volume of the cone =1/3πr²h
v/V=r²h/R²H=1/27
h=10R²/9r²
.................(equation 2)
on substituting the value of h from
equation 1 and 2 we get
30r/R=10R²/9r²
r³/R²=1/27
r/R = 1/3 substituting this in eq 1 we get
h=30×1/3
[ h=10cm]
h=Hr/R
h=30r/R
.................(equation 1)
volume of the cone =1/3πr²h
v/V=r²h/R²H=1/27
h=10R²/9r²
.................(equation 2)
on substituting the value of h from
equation 1 and 2 we get
30r/R=10R²/9r²
r³/R²=1/27
r/R = 1/3 substituting this in eq 1 we get
h=30×1/3
[ h=10cm]
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The height of a cone is 30 cm. A small cone is cut-off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?
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The height of a cone is 30 cm. A small cone is cut-off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The height of a cone is 30 cm. A small cone is cut-off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a cone is 30 cm. A small cone is cut-off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?.
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