Advertisements
Advertisements
Question
Choose the correct alternative answer for the following question.
A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.
Options
15 cm
10 cm
18 cm
5 cm
Advertisements
Solution
The radius of the cone = Radius of the cylinder = r cm (Say)
Height of the cylinder, h = 5 cm
Let the height of the cone be H cm.
It is given that the cone melted and recasted into a cylinder.
∴ Volume of the cone = Volume of the cylinder
\[\Rightarrow \frac{1}{3}\pi r^2 H = \pi r^2 h\]
\[ \Rightarrow H = 3h\]
\[ \Rightarrow H = 3 \times 5 = 15 cm\]
Thus, the height of the cone is 15 cm.
APPEARS IN
RELATED QUESTIONS
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]
An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area (use π = 3.14 and `sqrt3=1.73)`
Four equal circles, each of radius 5 cm touch each other as shown in fig. Find the area included etween them.
A square water tank has its side equal to 40m, there are 4 semicircular flower beds grassy plots all around it. Find the cost of turfing the plot at Rs 1.25/sq.m
The circumference of a circle is 22 cm. Find the area of its quadrant.
In the given figure, OPQR is a rhombus, three of whose vertices lie on a circle with centre O. If the area of the rhombus is `32sqrt(3)`, find the radius of the circle.
The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is
Two circles touch each other externally. The sum of their areas is 5811 cm2 and the distance between their centres is 10 cm. Find the radii of the two circles.
The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm2 Find the radii of the two circles.
Find the circumference of the circle whose area is 81π cm 2.
The radius of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π =`22/7`)
The circumference of a circle is eigth time the circumference of the circle with a radius of 12 cm. Find its diameter.
The circumference of a circle exceeds its diameter by 18 cm. find the radius of the circle.
The circumference of a circle is numerically equal to its area. Find the area and circumference of the circle.
Diameters of different circles are given below. Find their circumference (Take π = `22/7`)
d = 28 mm
A wire of length 1320 cm is made into circular frames of radius 7 cm each. How many frames can be made?
The perimeter of circular and square fields is equal. If the area of the square field is 484 m2 then the diameter of the circular field is ____________.
The area of a quadrant of a circle whose circumference is 22 cm, is ____________.
Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.
