If a cone, a hemisphere and a right circular cylinder stand on equal b

1.	If a cone, a hemisphere and a right circular cylinder stand on equal base and have the same height then their volumes are in the ratio1). 2: 3: 22). 2: 3: 13). 1: 2: 34). 3: 2: 2
Answer» Let r be the radius of cone, cylinder and hemisphere And h be the height of cone, cylinder and hemisphere As we know, That height of a hemisphere is equal to radius of the hemisphere ∴ h = r Now, Volume of cone = $(\FRAC{1}{3}\;\PI {r^2}\;h = \;\frac{1}{3}\;\pi {r^3})$ Volume of cylinder = π r² h = π r³ Volume of hemisphere $(= \;\frac{2}{3}\;\pi \;{r^3})$ Now, required ratio= Volume of cone: volume of hemisphere: volume of cylinder ⇒ Required ratio $(= \;\frac{1}{3}\;\pi {r^3}:\;\frac{2}{3}\;\pi \;{r^3}:\;\pi \;{r^3}\; = \;\frac{1}{3}:\frac{2}{3}:1 = 1\;:2\;:3)$ Thus, the required ratio is 1: 2: 3

If a cone, a hemisphere and a right circular cylinder stand on equal base and have the same height then their volumes are in the ratio1). 2: 3: 22). 2: 3: 13). 1: 2: 34). 3: 2: 2

Answer»

Let r be the radius of cone, cylinder and hemisphere

And h be the height of cone, cylinder and hemisphere

As we know,

That height of a hemisphere is equal to radius of the hemisphere

∴ h = r

Now, Volume of cone = $(\FRAC{1}{3}\;\PI {r^2}\;h = \;\frac{1}{3}\;\pi {r^3})$

Volume of cylinder = π r² h = π r³

Volume of hemisphere $(= \;\frac{2}{3}\;\pi \;{r^3})$

Now, required ratio= Volume of cone: volume of hemisphere: volume of cylinder

⇒ Required ratio $(= \;\frac{1}{3}\;\pi {r^3}:\;\frac{2}{3}\;\pi \;{r^3}:\;\pi \;{r^3}\; = \;\frac{1}{3}:\frac{2}{3}:1 = 1\;:2\;:3)$

Thus, the required ratio is 1: 2: 3

Discussion

No Comment Found

Related InterviewSolutions

1). 56.822). 56.283). 57.824). 57.28
1). 1872). 2093). 1634). 149
If the area of a square A has area 24 cm2, then what is the area of another square B having diagonal two-third of the diagonal of A?1). 26 cm22). 42.5cm23). 32/3 cm24). 38.6 cm2
In a parallelogram, the lengths of the two adjacent sides are 12 cm and 14 cm respectively. If the length of one diagonal is 16 cm, find the length of the other diagonal.1). 14.6 cm2). 20.6 cm3). 18.3 cm4). 25.2 cm
The volume of the metal of a cylindrical pipe is 1496 cm3. The length of the pipe is 28 cm and its external radius is 18 cm. its thickness is approximately: (Take π = 22/7)1). 0.5 cm2). 10.4 cm3). 4.6 cm4). 7.4 cm
ABCD is a parallelogram. Co - ordinates of A, B and C are (5, 0), (- 2, 3) and (- 1, 4) respectively. What will be the equation of line AD?1). y = 2x - 52). y = x + 53). y = 2x + 54). y = x - 5
Find total surface area (in sq. cm) of a hollow globe with outer radius 18 cm and thickness 10 mm.1). 972 π2). 1552 π3). 2320 π4). 2452 π
If a cone, a hemisphere and a right circular cylinder stand on equal base and have the same height then their volumes are in the ratio1). 2: 3: 22). 2: 3: 13). 1: 2: 34). 3: 2: 2
Two circles of radius 9 cm and 8 cm touch externally. Find the distance between their centres?1). 17 cm2). 2 cm3). 9 cm4). 15 cm
A cylindrical shaped speaker of circumference 44 cm is wrapped around by a piece of paper of area 528 sq.cm. Find the volume of the speaker in cubic meters.1). 0.000772). 0.000963). 0.001284). 0.00225