A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Calculate the cost of cloth required to make the tent at the rate of Rs.80 per square meter.
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Hence, the curved surface area of the tent = 1034 m^{2}
Cost of canvas = Rs.(1034 × 80) = Rs. 82720
A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 in surmounted by a right circular cone of same base radius. Calculate the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m.
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The surface area of a sphere is 2464 cm^{2}. If its radius be doubled, find the surface area of the new sphere.
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If the total surface area of a solid hemisphere is 462 cm^{2}, calculate its volume.
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Two cubes each of volume 27 cm' are joined end to end to form a solid. Calculate the surface area of the resulting cuboid.
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The volume of a hemisphere is 2425.5 cm^{3 }. Calculate its surface area.
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The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, calculate its volume.
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The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km^{2}. Calculate the height of the mountain.
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If the volumes of two cones are in the ratio of 1: 4 and their diameters are in the ratio of 4 : 5, calculate the ratio of their heights.
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A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Calculate the cost of cloth used at the rate of Rs. 25 per metre.
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The volume of a cube is 729 cm^{3}. Calculate its surface area.
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A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km/hr. Find the amount of water (in cubic metres) that runs into the sea per minute.
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Calculate cubes of 10 cm edge can be put in a cubical box of 1 m edge?
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Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. Calculate the edge of the new cube formed.
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Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Calculate the volume of the resulting cuboid.
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Cuboid
1 |
Total Surface Area |
A |
2h(l+b) + lb |
2 |
Total Surface Area without lid |
B |
2h(l+b) |
3 |
Curved Surface Area |
C |
2(lb + bh + lh) |
4 |
Volume |
D |
Lbh |
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Answer :
1-C, 2-A, 3-B, 4-D
1 |
Total Surface Area of Sphere |
A |
3πr^{2} |
2 |
Volume of Sphere |
B |
23πr^{3} |
3 |
Total Surface Area of Hemisphere |
C |
43πr^{3} |
4 |
Volume of Sphere |
D |
4πr^{2} |
Answer :
1-D, 2-C, 3-A, 4-B
Answer :
1-A, 2-C, 3-B
Cylinder
1 |
Total Surface Area |
A |
πr^{2}h |
2 |
Total Surface Area without lid |
B |
2πr(h+r) |
3 |
Curved Surface Area |
C |
πr(2h+r) |
4 |
Volume |
D |
2πrh |
Answer :
1-B, 2-C, 3-D, 4-A
Cube
1 |
Total Surface Area |
A |
4s^{2} |
2 |
Total Surface Area without lid |
B |
6s^{2} |
3 |
Curved Surface Area |
C |
s^{3} |
4 |
Volume |
D |
5s^{2} |
Answer :
1-B, 2-D, 3-A, 4-C
Topics covered in Chapter 13, Surface Areas and Volumes are;
• The surface area of a combination of Solids
• The volume of a combination of solids
• Conversion of solid from one shape to another
• Frustum of a cone
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