Surface area of a solid

Q.

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere. [3 MARKS]

Q. Question 2
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Q. The dimensions of a solid iron cuboid are 4.4 m $\times 2.6m\times$ 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.

Q. The volume of the largest right circular cone that can be cut out from a cube of edge 7 cm is:

1. $79.8c{m}^3$
2. $79.4c{m}^3$
3. $89.8c{m}^3$
4. $89.4c{m}^3$

Q.

What is the meaning of total surface area of an object?

1. Total area of all surfaces the object has

2. Total area of surface of object that is visible to eye

3. Curved Surface Area

4. Curved Surface Area + Lateral Surface Area

Q.

A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. The surface area of the cylinder is

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Q.

The radius of the base and the height of a right circular cylinder are 7 cm and 13.5 cm respectively. The volume of the cylinder( in $c{m}^3$) is

1. 1579

2. 1897

3. 2079

4. 2197

Q. Question 6
From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Q. The formula for lateral surface area of a cylinder of radius 'r' and height 'h' is

1. $\pi r^{2}h$
2. $\pi rh$
3. $\pi rl$
4. $2\pi rh$

Q.

The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

1. πr²h

2. πR²h

3. π(R²-r²)h

4. π(R²+r²)h

Q.

If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in $c{m}^2$) is:

1. 82

2. 123

3. 164

4. 216

Q.

An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and for stitching. Give your answer to the nearest $m^2$ .

Q. A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.

Q.

Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see Fig.). If the base of the shed is of dimension 7 m × 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 $m^3$, and there are 20 workers, each of whom occupy about 0.08 $m^3$ space on an average. Then, how much air is in the shed (in $m^3$)? (Take $\pi =\frac{22}{7}$)

1. 800

2. 845.3

3. 900

4. 827.15

Q.

A cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid(in $c{m}^2$ ).

1. 332.5 $c{m}^2$

2. 346.8 $c{m}^2$

3. 312.5 $c{m}^2$

4. 320 $c{m}^2$

Q. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm , a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cms

Q. Question 5
Two identical cubes each of volume $64c{m}^3$ are joined together end to end. What is the surface area of the resulting cuboid?

Q.

A solid sphere of radius 10.5 cm is cut into 2 halves. Find the total surface area of both the hemispheres.

Q.

A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. The surface area of the cylinder is

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Q. A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use $\mathrm{\pi }$ = 3.14] [CBSE 2015]

Q.

A boy is trying to catch fish sitting at a height of 12 m from the surface of the water.A big fish is at a horizontal distance of 5 m from him. What should be the length of his string to get the fish?

1. 13

2. 10

3. 7

4. 15

Q. a circular lamina is divided into two parts which makes two distinct right circular cones such that theirarea conical surfaces are in the ratio 2:1. find the ratio of their volumes?

Q. How many balls, each of radius I cm, can be made from a solid sphere of lead of radius 8 cm?

Q.

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy( in $c{m}^2$) if the height of the conical part is 12 cm.

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Q.

A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, is surmounted by a cone of equal base and height 2.8 m. Find the cost of canvas required for making the tent at ₹100 per sq.m.

1. ₹ 6590

2. ₹ 7590

3. ₹ 9876

4. ₹ 8590

Q.

If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in $c{m}^2$) is

1. 164

2. 82

3. 123

4. 216

Q.

A road roller was used for levelling a road of width 2 m. It was observed that, the road roller required 25 complete revolutions to level the entire road. If the radius and the length of the roller is 7 m and 2 m respectively, then length of the road is ____. [Take $\pi$ = 3.14].

1. 1200 m

2. 2100 m

3. 1100 m

4. 1234 m

Q.

A Cuboid has length, breadth and height of 6cm, 4 cm and 2 cm respectively. The total surface area of Cuboid is

1. 22

2. 44

3. 176

4. 88

Q. The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.

1. $3300c{m}^2$
2. $1914c{m}^2$
3. $1386c{m}^2$
4. $26720c{m}^2$

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

1. 50 $c{m}^3$

2. 66 $c{m}^3$

3. 75 $c{m}^3$

4. 62 $c{m}^3$