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Published on: 18/09/2019
Surface Areas and Volumes
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1.
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m, how much concrete mixture would be required to build 14 such pillars?
2.
A storage tank is in the form of a cube, when full has the volume of water as 15.625 m3. If the present depth of water is 1.3 m, find the volume of water already used from the tank.
3.
The length of a room is double its breadth. Its height is 3 m. The area of the four walls excluding a door of dimensions 4 m \(\times \) 2 m is 100 m2. Find its volume.
4.
A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs 5 per 100 cm2. \(\left( Take\ \pi =\frac { 22 }{ 7 } \right) \)
5.
Find
(i) the curved surface area and
(ii) the total surface area of a hemisphere of radius 21 cm.
6.
Find the surface area of a sphere of radius 7 cm.
7.
The radius and height of a right circular cone are in the ratio 4 : 3. If the area of the base of the cone is 154 cm2, find the area of its curved surface. \(\left[ Use\ \pi =\frac { 22 }{ 7 } \right] \)
8.
What is the radius and curved surface of a cone made from a quadrant of a circle of radius 28 cm?
9.
The diameter of a circular wall is 4.5 m and its depths is 14 m.Find the cost of cementing the inner surface of the wall at Rs. 120 per sq. m.
10.
A right circular cylinder is 3 m high and the circumference of its base is 22 m.Find its curved surface area.
11.
The floor of a rectangular hall has a perimeter of 250 m and its length and breadth are in the ratio of 13: 12. If the cost of painting the four walls and ceiling at the rate of Rs. 5 per m2 is Rs.27000, find the height of the hall.
12.
The length, breadth, and height of a cuboid are 15 cm, 10 cm, and 20 cm. Find the surface area of the cuboid.
13.
The edge of a cube is 10.5 mm. Find its total surface area in cm2.
1.
Since the concrete mixture that is to be used to build up the pillars is going to occupy the entire space of the pillar, what we need to find here is the volume of the cylinders.
Radius of base of a cylinder = 20 cm
Height of the cylindrical pillar = 10 m = 1000 cm
So, volume of each cylinder = \(\pi\)r2h
\(=\frac{22}{7} \times 20 \times 20 \times 1000 \mathrm{~cm}^{3}\)
\(=\frac{8800000}{7} \mathrm{~cm}^{3}\)
\(\left.=\frac{8.8}{7} \mathrm{~m}^{3} \text { (Since } 1000000 \mathrm{~cm}^{3}=1 \mathrm{~m}^{3}\right)\)
Therefore, volume of 14 pillars = volume of each cylinder x 14
\(=\frac{8.8}{7} \times 14 \mathrm{~m}^{3}\)
= 17.6 m3
So, 14 pillars would need 17.6 m3 of concrete mixture.
2.
7.5 m3
3.
216 m3
4.
Since only the rounded surface of the dome is to be painted, we would need to find the curved surface area of the hemisphere to know the extent of painting that needs to be done. Now, circumference of the dome = 17.6 m. Therefore, 17.6 = 2\(\pi\)r.
So, the radius of the dome \(=17.6 \times \frac{7}{2 \times 22} \mathrm{~m}=2.8 \mathrm{~m}\)
The curved surface area of the dome = 2\(\pi\)r2
\(=2 \times \frac{22}{7} \times 2.8 \times 2.8 \mathrm{~m}^{2}\)
= 49.28 m2
Now, cost of painting 100 cm2 is RS. 5.
So, cost of painting 1 m2 = RS. 500
Therefore, cost of painting the whole dome
= RS. 500 x 49.28
= RS. 24640
5.
(i) The curved surface area of a hemisphere of radius 21 cm would be
\(=2 \pi r^{2}=2 \times \frac{22}{7} \times 21 \times 21 \mathrm{~cm}^{2}=2772 \mathrm{~cm}^{2}\)
(ii) the total surface area of the hemisphere would be
\(3 \pi r^{2}=3 \times \frac{22}{7} \times 21 \times 21 \mathrm{~cm}^{2}=4158 \mathrm{~cm}^{2}\)
6.
The surface area of a sphere of radius 7 cm would be
\(4 \pi r^{2}=4 \times \frac{22}{7} \times 7 \times 7 \mathrm{~cm}^{2}=616 \mathrm{~cm}^{2}\)
7.
192.5 cm2
8.
7 cm, 616 cm2
9.
Rs. 23760
10.
66 m2
11.
21.6 m
12.
1300 cm2
13.
6.615 cm2
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