Unit - 7 Prism and Pyramid- Grade X

Unit - 7

Prism and Pyramid

Exercise (7.3)

Solved Questions

1.    

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3.  

  

Exercise (7.3) with Answers

4.    The volume of a square based pyramid is 120 cm³. If its height is 10cm, find the length of its base. (6cm) 

5.    If the slant height of a triangular face of a square based pyramid of side 16cm is 17cm, find the volume of the pyramid. (1280cm³)

6.    Find the total surface area of a square based pyramid having vertical height 8cm and height of the triangular faces 10cm. (384cm²)

7.    Find the lateral surface area and the volume of a square based pyramid where length of the side of the base is 12cm and the vertical height is 8cm. (240cm², 384cm³)

8.    Volume of a square based pyramid is 128 cm³. If the vertical height and the length of the side of square base are in the ratio of 3:4, find the total surface area of the pyramid. (179.37cm²)

9. The total surface area of a square based pyramid is 340cm² and the length of slant height is 12cm, find the length of the side of base. (10cm)

10. The volume of a square based pyramid in 2400 cm² and its height is 8cm. Find the total surface area of the pyramid. (1920cm²)

11. The total surface area of a square based pyramid is 1920 cm² and the length of side base is 30cm. Find the vertical height of the pyramid. (8cm)

Exercise (7.4)

Combined Solids

Solved Questions

1.    Find the surface area and volume of the solid shown in the figure which is the combination of a cylinder and a hemisphere.

     

2.    Find the total surface area and volume of the given solid, which is the combination of a cylinder and a cone.

3.    Find the surface area and volume of the combined solid formed by cone and hemisphere given in the figure.

 

4.    A solid consist double cone each of vertical height 10.5 cm and slant height 11.9cm. Find the surface area and volume of the solid.

5.    Find the volume of the material of the given cylindrical pipe if the base area of the hollow space as shown in the figure is maximum. 

Exercise (7.4) with Answers

6.    The total surface area of a given solid is 770cm² and total height is 14cm. Find the height of the cylinder. 

 7cm

7.    The total surface area of a given solid is 1078cm² and total height is 21cm. Find the height of the cylinder. 

 14cm

8.    A tent is in the shape of a right circular cylinder of height 4m. with a cone of height 3m. over it. Find the total surface area of the tent.

  163.42 m²

9.    A tent is in the shape of a right circular cylinder of height 9m. and a cone of height 8m. and slant height 10m. over it, find the total surface area of the tent.
528 m²

10. The volume and base area of a given figure are 600cm3 and 100cm² respectively. If the height of the cylinder is 5cm, find the total height of the solid. 
8cm

11. The total height of the solid object given alone side is 30cm. If the height of the cone and cylinder is in the ratio of 2:3, find the total volume of the solid object.  
1251.58cm³

12. The ratio of the slant height and the radius of a conical part of the given combined solid is 5:3. The total volume of the given solid is 240πcm3. Calculate the total surface area of the solid.
   414.86 cm²

13. The ratio of slant height and vertical height of the conical part of the given combined solid object is 13:12. The total surface area of the solid is 840πcm². Calculate the volume of the given solid object.
.  11628.57 cm³

14. From a solid cylinder of height 12cm and base radius 5cm, a conical cavity of the same height and base is hollowed out. Find the surface area of the remaining solid. 581.43cm²

15. A circus tent is cylindrical in shape up to the height of 12.5m and conical above it. If the diameter of the tent is 16m and height of the conical part is 15m, find the surface area of the tent.  1257.14cm²

16. A solid object is made of hemisphere and a cone. If the total height of the object is 14.6cm and height of the conical part is 9cm, find the surface area of the object. 383.68cm²

17. A conical hole of base and height equal to a cylindrical wooden log is drilled out. Find the height of the log and volume of the remaining part. 
216.83cm²