Unit-7 Prism and Pyramid- Grade X

Unit-7 

Prism and Pyramid

Exercise (7.1)

Solved Questions

1.    Find the volume of the following triangular prisms:

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Exercise (7.1) with Answers

1.    Find the volume of the following triangular prisms:

Ans: a) 1080cm³ b) 4500cm³ c) 180cm³

2.    If the perimeter of the base of a triangular prism is 18cm and its height is 15cm, find the lateral surface area of the prism. (270cm²)

3.    If the area of the base of a triangular prism is 18.4cm² and its length 35cm, find the volume of the prism. (644cm²)  

4.    The area of the base of a triangular prism is 28.5cm². If its lateral surface area is 300 cm², find the total surface area of the prism. (357cm²)

5.    If the perimeter of the base of a triangular prism is 15.5cm and its lateral surface area is 248 cm², find the length of the prism. (16cm)

6.    The volume of a prism with equilateral triangular cross-section is 270cm3.If the length of the prism is 10√3cm, what is the length of the side of the equilateral triangular cross-section? (6cm)

7.    If height of the right-angled isosceles triangular based prism with volume 2000 cubic cm is 40cm, find the length of its sides. (10cm,10cm,10√2cm)

8.    Find the volume of a prism having triangular base of sides 10cm, 17cm and 21cm and length 25cm.(2100cm³)

9.    If the sides of the base of a triangular prism are 3cm, 4cm, and 5cm and total surface area is 156 square cm, find its height and volume. (12cm,72 cm3)

10. The cross-section of a triangular prism is a right-angled isosceles triangle with one of the equal side 6cm. If the length of the prism is 8 2 cm, calculate the total surface area and volume of the prism. (267.76cm², 203.65cm³)

Exercise (7.2)

Solved Questions

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Exercise (7.2) with Answers

6.    Find the curved surface area, total surface area and volume of the following right cones.

Ans: a) 220 cm², 374cm² b) 550cm², 704cm² c) 57.75cm³

7.    Find the volume of the cone having vertical height 27cm and radius 7cm. (1386ccm³)

8.    A cone has diameter of its base 14cm and slant height 25cm. Find its volume. (1232 cm³)

9.    Find the total surface area of a cone whose radius of base 13cm and height 84cm.(4004cm²) 

10. The diameter of the circular base of a cone is 12cm and its vertical height is 8cm. Find the total surface area of the cone. (301.71cm²)

11. Find the curved surface area of a cone whose slant height and vertical height are 35cm and 28cm respectively. (2310cm²)

12. Find the vertical height and volume of a right circular cone with slant height 25cm and curved surface area 550cm². (24cm, 1232cm³)

13. If the radius of a right circular cone is 4cm and curved surface area 62.8cm², find its volume. [π = 3.14] (50.28 cm³)

14. Find the height of the cone whose volume is 1232cm³ and diameter of its circular base is 14cm. (24cm)

15. A right circular cone of height 21cm has a volume of 1078cm³. Calculate the diameter of the base of the cone. (14cm)

16. Volume of a cone is 513.33cm³ and its vertical height is 10cm. Calculate the circumference of the base. (44cm)

17. Total surface area of a cone is 594cm² and its slant height 20cm. Find the diameter of its base. (14cm)

18. Curved surface area of a cone is 2200cm². If its slant height is 50cm, find the height of the cone. (48cm)

19. Curved surface area of a right circular cone is 8800cm² and diameter of its base is 56cm. Find its height. (96cm)

20. Total surface area and curved surface area of a cone are 770cm² and 550cm² respectively. Find its radius. (8.36cm)

21. Total surface area and curved surface area of a cone are 1320cm² and

704cm², find its radius. (16cm)