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 Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use `pi=22/7`]
A wire is looped in the form of a circle of radius 28 cm. It is re-bent into a square form. Determine the length of the side of the square.
The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in one minute. (Use π = 22/7)
In the given figure, ∆ ABC is a right-angled triangle in which ∠ A is 90°. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region
A car travels 1 km distance in which each wheel makes 450 complete revolutions. Find the radius of wheel.
An arc of length 20𝜋 cm subtends an angle of 144° at centre of circle. Find the radius of the circle.
The minute hand of a clock is √21 𝑐𝑚 long. Find area described by the minute hand on the face of clock between 7 am and 7:05 am
A playground has the shape of rectangle, with two semicircles on its smaller sides as diameters, added to its outside. If the sides of rectangle are 36m and 24.5m. find the area of playground.
Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.
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.
A horse is tied with a 21 m laig rope to the corner of a field which is in the shape of an equilateral triangle. Find the area of the field over which it can graze.
The diameter of a circle is 28 cm.
Find its :
(i) Circumference
(ii) Area.
In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region.
Sum of the areas of two squares is 157 m2. If the sum of their perimeters is 68 m, find the sides of the two squares.
The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take π =`22/7`)
Complete the table below.
| Radius (r) | Diameter (d) | Circumference (c) |
| ...... | ...... | 72.6 cm |
Diameters of different circles are given below. Find their circumference (Take π = `22/7`)
d = 70 cm
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 ____________.
Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?
Ratio of the circumference of a circle to its diameter is denoted by symbol ______.
