Advertisements
Advertisements
प्रश्न
A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.
उत्तर
lnternal radius of the hollow cylinder = r = 3.5 cm
Height = h = 21 cm
Thickness of the metal = 0.5 cm
Therefore, Outer radius= R = (3.5+0.5) cm = 4 cm
Now, Volume of metal used = `pih(R^2 - r^2)`
= `22/7 xx 21 xx (4^2 - 3.5^2)`
= `22/7 xx 21 xx (16 - 12.25)`
= `22/7 xx 21 xx 3.75`
= 247.5 cm3
Volume of metal used = 247.5 cm3
Therefore, Volume of cone= 247.5 cm3 and height = 7 cm
Let r1 be the radius of cone.
∴ Volume = `1/3pir1^2h`
⇒ `1/3 pir1^2h = 247.5`
⇒ `1/3 xx 22/7 xx r1^2 xx 7 = 247.5`
⇒ `r1^2 = (247.5 xx 3 xx 7)/(22 xx 7)`
⇒ `r1^2 = 33.75`
⇒ `r1 = 5.8 "cm"`
Radius of the cone = 5.8 cm
APPEARS IN
संबंधित प्रश्न
In Figure , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]
If the perimeter of a semi-circular protractor is 66 cm, find the diameter of the protractor (Take π = 22/7).
The circumference of a circle exceeds diameter by 16.8 cm. Find the circumference of
circle.
A field is in the form of circle. A fence is to be erected around the field. The cost of fencing would to Rs. 2640 at rate of Rs.12 per metre. Then the field is to be thoroughs ploughed at cost of Rs. 0.50 per m2. What is amount required to plough the field?
An arc of length 20𝜋 cm subtends an angle of 144° at centre of circle. Find the radius of the circle.
The outer circumference of a circular race track is 528m. The track is everywhere 14m
wide. Calculate the cost of leveling the track at rate of 50 paise per square metre.
Three equal circles, each of radius 6 cm, touch one another as shown in the figure. Find the area of enclosed between them.
The radius of the circle is given below; find the area.
28 cm
Find the curved surface area , the total surface area and the volume of a cone if its :
Height = 8 cm , diameter = 12 cm
The area between the circumferences of two concentric circles is 2464 cm2. If the inner circle has circumference of 132 cm, calculate the radius of outer circle.
Find the area and perimeter of the following semi-circle :
Radius= 1.4 cm
Find the volume and the surface area of the spheres in the following :
Radius = 7 cm
The diameter of a circle is 28 cm.
Find its :
(i) Circumference
(ii) Area.
The radii of two circles are 25 cm and 18 cm. Find the radius of the circle which has a circumference equal to the sum of circumferences of these two circles.
What is the circumference of a circle of diameter 10 cm (Take π = 3.14)?
If the circumference of a circle is 82π, then the value of ‘r’ is
Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.
Ratio of the circumference of a circle to its diameter is denoted by symbol ______.
The circumferences of two circles are in the ratio 4 : 5. What is the ratio of their radii?
