Surface area and Volume
Case Study 4:- The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of India Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BC. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha . It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal stucture mounted on it. (Take π = 22/7)
(i) Calculate the volume of the hemispherical dome if the height of the dome is 21 m.
(a) 19404 cu. m (b) 2000 cu. m
(c) 15000 cu.m (d) 19000 cu.m
(ii) The formula to find the volume of sphere is
(a) 
(b) 
(c) 
(d) 
(iii) The cloth required to cover the hemispherical dome if the radius of its base is 14 m, is
(a) 1222 sq.m (b) 1232 sq.m
(c) 1200 sq.m (d) 1400 sq.m
(iv) The total surface area of the combined figure i.e. hemispherical dome with radius 14 m and cuboidal shaped top with dimensions 8m×6m×4m is
(a) 1200 sq.m (b) 1232 sq.m
(c) 1392 sq.m (d) 1932 sq.m
(v) The volume of the cuboidal shaped top with dimensions mentioned in question (iv) above, is
(a) 182.45 m³ (b) 280.45 m³
(c) 292 m³ (d) 192 m³
Solution:- (i) Answer (a)
Explanation:- Height of the dome = Radius of the dome = 21 m
i.e., h = r = 21 m
Volume of the hemispherical dome =
= 19404 cu.m
(ii) Answer (b)
Explanation:- Volume of sphere =
(iii) Answer (b)
Explanation:- The cloth required to cover the hemispherical dome = Curved surface area of dome
= 2πr²
= 
sq.m
(iv) Answer (c)
Explanation:- Total surface area of the combined dome with cuboidal shaped top
= C.S.A. of dome + 2(lb + bh + lh) – l×b
= 1232 + 2(48 + 24 + 32) – 48
= 1392 sq.m
(v) Answer (d)
Explanation:- Volume of the cuboidal shaped top = l×b×h
= 8×6×4
= 192 m³
Case Study 1:- A circus is a company of performers who put on shows of acrobats, clawns etc, to entertain people started around 250 years back, in open fields, now generally performed in tents.
One such ‘Circus Tent’ is shown below.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part, then find:
(i) What is the radius of conical part ?
(ii) The area of canvas used in making the tent.
OR
Find the slant height of the cone.
(iii) The cost of canvas bought for the tent at the rate $ 200 per sqm, if 30 sqm canvas was wasted during stitching.
Solution:- See full solution
Case Study 2:- A school mathematics teacher took her class x students on an educational trip to show Gol Gumbaz. The teacher had an interest in history as well. She told children about the history of Gol Gumbuz. Gol Gumbaz is the tomb of king Muhammad Adil shah. The construction of this tombwas started in 1626 and completed in 1656. The teacher then stated that this monument contains a combination of solid figures. She pointed that there are a cubical bases and a hemispherical dome is at the top.
(i) If one side of the cubical portion is 23 m, then what is the diagonal of the cubic portion of the Gol Gumbaz ?
(ii) A block of Gol Gumbaz is in thee shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the shape is 2 cm. What is the volume of the block ?(Use π = 3.14)
OR
Find the total surface area of Gol Gumbaz.
(iii) What is the curved surface area of the new solid formed by joining two solid hemispheres of same radii their bases ?
Solution:- See full solution
Case Study 3:- Adventure camp are the perfect place for the children to practice decision making for themselves without parents and teachers guiding their every move. Some students of a school reached for adventure at Sakleshpur. At the camp, thewaiters served some students with a welcome drink in a cylindrical glass and some students in a hemispherical cup whose dimensions are shown below. After that they went for a jungle trek. The Jungle trek was enjoyable but tiring. As dusk fell, it was time to take shelter. Each group of four students was given a canvas of area 551 m². Each group had to make a conical tent to accommodate all the four students. Assuming that all the stitching and wasting incurred while cutting, would amount to 1 m², the students put the tents. The radius of the tent is 7 m.
(i) The volume of cylindrical cup is