Cones

Q.

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete.

Each step has a rise of m and a tread of m (See figure) calculate the total volume of concrete required to build the terrace.

Q. A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire.
[CBSE 2012]

Q. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Q.

The diameter of a shot put is 9 cm. Calculate the volume of the shot-put.

Q. 48. A solid right circular cone if radius 3 cm and slant height 5 cm is cut by a plane through the vertex of the cone into 2 exact pieces. Find the TSA of a single piece

Q.

The base edges of two square pyramid are in the ratio 1 : 2 and their heights are in the ratio 1 : 3. The volume of the first pyramid is 180 cubic centimetres. What is the volume of the second?

Q.

In two square pyramids of the same volume, the base edge of one is half the base edge of the other. How many times the height of the pyramid with larger base is the height of the other?

Q. 66 cubic cm of silver is drawn into a wire 1 mm in diameter. Calculate the length of the wire in metres.

Q. A beam 4 m long, 50 cm wide and 20 cm deep is made of wood which weighs 25 kg per m³. Find the weight of the beam.

Q. Assertion (A)
The number of coins of diameter 1.75 cm and 2 mm thickness that can be formed from a melted cuboid (10 cm × 5.5 cm × 3.5 cm) is 400.

Reason (R)
Volume of a cylinder of base radius r and height h $=\left(\mathrm{\pi }{r}^{2}h\right)$ cubic units. And area of a cuboid = (l × b × h) cubic units.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q.

Grains of fine beach sand are approximately spheres with an average radius of 50 micro meter and are made of silicon di oxide, which has a density of 2600 kg/m ³. What mass of sand grains would have a total surface area ( the total area of all the individual spheres) equal to the surface area of a cube 1m on an edge?

Q. The cuboid water tank has length 2 m, breadth 1.6m and height 1.8m. Find the capacity of the tank in litres.

Q. 8. A solid right circular cone if radius 3 cm and slant height 5 cm is cut by a plane through the vertex of the cone into 2 exact pieces. Find the TSA of a single piece

Q.

In two square pyramids of the same volume, the base edge of one is half the base edge of the other. How many times the height of the pyramid with larger base is the height of the other?

Q. A 10 m deep well of diameter 1.4 m is dug up in a field and the earth from digging is spread evenly on the adjoining cuboid field. The length and breadth of that field are 55m and 14m respectively. Find the thickness of the earth layer spread.

Q.

To fill a 4 m wide, 8 m long and 3 m deep sand box, how much sand do you need?

1. 96 cubic metres

2. 150 cubic metres

3. 200 cubic metres

4. 32 cubic metres

Q.

A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm³ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?

Q. A 36 m-long, 15 broad verandah is to be paved with stones, each measuring 6 dm by 5 cm. How many stones will be required?

Q. The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 128 m³. The breadth of the wall is
(a) 30 cm
(b) 40 cm
(c) 22.5 cm
(d) 25 cm

Q.

What is the volume of a rectangular box, which is 2 feet high, 6 feet wide and 6 feet long?

1. 72 Cubic Feet

2. 36 Cubic Feet

3. 12 Cubic Feet

4. 14 Cubic Feet

Q. If the volume of a marble box of dimensions 28 x 5 x h is 280 units, then what is the value of h?

1. 7.5
2. 2
3. 6.5
4. 6

Q.

The volume of a 4 inches wide and 3 inches high box is 36 cubic inches, what is its length?

1. 4 Inches

2. 2 Inches

3. 9 Inches

4. 3 Inches

Q. Which among the given options correctly represents the pair of figures we get when we cut open the right circular cone(closed at the bottom) of radius(r) and slant height(l)?

1. None of the above
2. 
3. 
4. 

Q. If the volume of a rectangular block is 9000 cubic centimeter, then the length of its side is ___ cm.

1. 40
2. 30
3. 450
4. 300

Q. A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

Q.

The diameter of a shot put is 9 cm. Calculate the volume of the shot-put.