Advertisements
Advertisements
Question
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per 100 sq. cm. [Use π = 3.14]
Advertisements
Solution
Side of the cubical block, a = 10 cm
Longest diagonal of the cubical block = a√3 = 10√3 cm
Since the cube is surmounted by a hemisphere, therefore the side of the cube should be equal to the diameter of the hemisphere.
Diameter of the sphere = 10 cm
Radius of the sphere, r = 5 cm
Total surface area of the solid = Total surface area of the cube – Inner cross-section area of the hemisphere + Curved surface area of the hemisphere
`=6a^2-pir^2+2pir^2`
`=6a^2+pir^2`
`=6xx(10)^2+3.14xx5^2`
`=600+78.5=678.5 cm^2`
Total surface area of the solid = 678.5 cm2
Cost of painting 100 cm2 = Rs. 5
Cost of painting 1 cm2 = Rs.5/100
Cost of painting the total surface area of the solid =(5/100)× 678.5 = Rs. 33.925 ≈ Rs. 34.
APPEARS IN
RELATED QUESTIONS
A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm2
A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=22/7]`
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is ______.
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
