Today is our topic of discussion Solid Geometry exercises -13.
Solid Geometry exercises -13
1. A rectangular parallelepiped’s length is 5 cm, width 4 cm and height 3 cm. What’s its diagonal?
1) 5√2 cm
2) 25 cm
3) 25√2 cm
4) 50 cm
2. Lengths of other two sides except the hypotenuse of a right-angled triangle are 4 cm. and 3 cm. If the triangle is revolved about the larger side, the evolved solid will be a
(i) right circular cone
(ii) right circular cylinder
(iii) the area of the base of the evolved solid is 9π square centimetres
Which one of the above sentences is correct?
1) i
2) ii
3) i iii
4) ii iii
Answer to the questions 3 and 4 according to the informations given below. A spherical ball of diameter 2 cm. exactly fits in a cylindrical box
3. What is the volume of the cylinder? 1) 2π сc
2) 4π cc
3) 6п сс
4) 8π cc
4. What is the volume of the unoccupied portion of the cylinder? 2π
1) П сс
2) 3 CC
3) 4π 3 CC
4) Зп 3 CC
Answer to the questions 5 and 6 according to the informations given below. A metallic solid sphere of diameter 6 cm. is melted and a right circular cylinder the radius of whose base is 3 cm. is made.
5. What is the height of the cylinder made?
1) 4 cm
2) 6 cm
3) 8 cm
4) 12 cm
6. What is the area of the curved surface of the cylinder in square centimeters?
1) 24π
2) 42π
3) 72π
4) 96π
(Calculator can be used. If required, you can assume = 3.1416)
7. The length, breadth and height of a rectangular parallelopiped are respectively 16 metres 12 meters and 4.5 metres. Find the area of its surfaces, volume and length of a diagonal.
8. A rectangular tank of length 2.5 metres, breadth 1.0 metre stands on the ground. If its height is 0.4 meter, find the volume and its area of the interior surface.
9. Find the area of the whole surface of the cube whose edge is equal to the diagonal of the rectangular solid whose dimension are 5, 4 and 3 cm.
10. A hostel building is to be constructed for 70 students in which each student gets 4.25 square metres of floor and 13.6 cubic metres of space. If the hostel room is 34 metres long, what will be its breadth and height?
11. If the height of a right circular cone is 8 cm and the radius of its base is 6 cm, find the area of the whole surface and the volume.
12. The height of a right circular cone is 24 cm. and its volume is 1232 cubic cm. What is its slant height?
13. The length of two sides at the right angle of a right-angled triangle is 5 cm. and 3.5 cm. Find the volume of the solid formed by revolving it about its greater side.
14. Find the surface and volume of a sphere of radius 6 cm.
15. Three spherical balls of glass of radii 6, 8 and r cm. are melted and formed into a single solid sphere with radius 9 cm. Find the value of r.
16. The outer diameter of a hollow sphere is 13 cm. and the thickness of the iron is 2 cm. A solid sphere is formed with the iron used in the hollow sphere. What will be its diameter?
17. A solid sphere of radius 4 cm. is melted and formed into a uniform hollow sphere of outer radius 5 cm. Find the thickness of the second sphere.
18. The radius of a solid sphere of iron is 6 cm. With the iron contained in it, how many solid cylinders of length 8 cm. and diameter of the base 6 cm. can be formed?
19. A spherical ball of radius cm. exactly fits into a cubical box. Find the volume of the unoccupied portion of the box.
20. A sphere of radius 13 cm. is cut off by a plane perpendicular to its diameter through a point at a distance 12 cm. from the centre. Find the area of the plane formed.
21. The outer length, breadth and height of a wooden box with top are respectively 1.6, 1.2 and 0.8 metres and its wood is 3 cm. thick. What is the area of the inner surface of the box? What will be the cost of painting the inner surface of the box at the rate of Tk. 14.44 per square metre?
22. How many bricks each of length 25 cm., breadth 12.5 cm. and 8 cm. will be required to construct a wall of height 2 metres and thickness 25 cm. around a rectangular garden with length 120 metres and width 90 metres?
23. The length and breadth of a rectangular solid are in the ratio 4 : 3 and its volume is 2304 cubic centimetres. The total cost of making a solid with lead coating at the bottom at Tk. 10 per square centimetre is Tk. 1920. Find the dimensions of the solid.
24. A conical tent has a height of 7.50 metres. How much canvas will be required if it is desired to enclose a land of 2000 square metres?
25. Lengths of two sides of a prism with a pentagonal base are 6 cm. and 8 cm. and the length of each of the other three sides is 10 cm., height is 12.5 cm.
Find the total area of the surfaces and the volume of the prism.
26. The height of a regular hexagonal prism having side of 4 cm. is 5 cm. Find the total area of surfaces and the volume.
27. A pyramid is situated on a regular hexagon of side 6 cm. and its height is 10 cm. Determine the total area of surfaces and the volume.
28. If the length of an edge of a regular tetrahedron is 8 cm., find the total area of surfaces and the volume.
29. The lower part of a construction is a parallelopiped of length 3 metres and the upper part is a regular pyramid. If the base of the pyramid is of side 2 metres and the height is 3 metres, find the total area of surfaces and the volume of the construction.
30. A godown of two-part roof is constructed on a land of length 25 metres and width 18 metres. Its height is 5 metres. Each part of the roof is of 14 metres wide. Find the volume of the godown.
31. 1) Find the total area of surfaces of the solid shown in the diagram.
2) Find the approximate number (to the nearest integer) of solid spheres of diameter 1.8 cm which can be made after melting a cube whose sides are equal to the diagonal of the solid.
32. The diameter of the base of a tent like a right circular cone is 50 metres and its height is 8 metres.
1) Find the slant height of the tent.
2) How much land in square metres will be required to construct the tent? Find the volume of the vacuum space inside the tent.
3) What will be the cost of the canvas of the tent if its price is Tk. 125 per square metre?
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