Wednesday, 7 October 2015

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Surface Area and Volume of Combination of Solids

Surface Area and Volume of Combination of Solids
 knowledge philic presents....

with a view to crack tier-2 , today we uploaded the questions of solid figure which is very important for ssc and these are the best collection of solid geometry. solve it and build your confidence 

formula of pyramid

1. Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm?

2. From a right circular cylinder with height 10 cm and radius of base 6 cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid?

3. A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter
of the base of the cone is 6 cm and its height is 4 cm. Find the cost of painting the toy at
the rate of Rs 7 per 100 cm square?
(Use pi = 22/7)

4. Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the
diameter of the top is 3.5 cm. Find the area he has to colour.
(Take pi = 22/7)

5. A wooden show-piece is of the shape of  cylinder surmounted by a hemisphere. The
diameter of the cylinder is 42 cm and its height is 40 cm. Find the cost of polishing
the surface area of the show-piece at the rate of Rs 10 per 1000 cm2 (excluding the base of
the show-piece)?

6. From the figure given below, find the volume of the toy.

7. A sphere has a diameter of 500√ 3 cm. A biggest cube is fitted in it. Now a biggest
sphere is fitted within this cube. Again a biggest cube is fitted within this smaller
sphere. Determine the ratio of volume of bigger cube to the volume of smaller cube?

8. A circus tent is cylindrical upto a height of 7 m and conical above it. The diameter of the cylindrical portion is 10 m and the total height of the tent from ground to the vertex of the conical part is 19 m. Find the cost of canvas required to build the tent at the rate of Rs 7.70 per square metre?
(Use pi = 22/7)

9. A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is ¼ of its height. Find the volume and total surface area of the solid?
(Use pi = 22/7)

10. The decorative block shown in the figure is made of two solids—a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface of the block.
(Take pi = 22/7)

11.  A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in the above figure. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours.
(Take pi= 3.14)

12. Mayank made a bird-bath for his garden in the shape of a cylinder with a hemisphere
depression at one end (see the figure). The height of the cylinder is 1.45 m and its radius
is 30 cm. Find the total surface area of bird bath?
(Take pi = 22/7)

13. Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see the figure). If the base of the shed is of dimension 7m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of 300 m3, and there are 20 workers, each of whom occupy about 0.08 m3 space on an average. Then how much air is in the shed?
(Take pi = 22/7)

14. A juice sellor was serving his customers using glasses as shown in the given figure. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemisphere raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity.
(Take pi = 3.14)

solve all these questions and share your ans........match with our ans key....will upload soon...feel free to share your doubts and query.

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