Advertisements
Advertisements
Question
The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
Options
2π : 1
4π : 1
3π : 1
1 : 4π
Advertisements
Solution
The ratio of total surface area of a solid hemisphere to the square of its radius is 3π : 1.
Explanation:
Curved Surface Area = 2πr2
Curved Surface Area of Hemisphere = `(1/2) 4πr^2 = 2πr^2`
Base Area of a hemisphere = πr2
Total Surface Area of Hemisphere = 2πr2 + πr2 = 3πr2
Divide the total surface area by r2
`= (3pir^2)/r^2`
`= 3pi`
Therefore, the ratio of the total surface area of a solid hemisphere to the square of its radius is 3π : 1
APPEARS IN
RELATED QUESTIONS
In Figure 2, ABCD is a trapezium of area 24.5 sq. cm. In it, AD|| BC, ∠ DAB = 900, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region. [Take π=22/7]
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid [take π=22/7]
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π = `22/7`]
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
1) The area of the metal sheet used to make the bucket.
2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]
Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
A plumbline (sahul) is a combination of
If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
