Cube and Its Surface Area

Q. Water flows at the rate of 10m/min through a cylindrical pipe of 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Q.

A heap of rice is in the form of a cone with a diameter of 9m and a height of 3.5m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Q.

A 3 x 3 Rubik's cube has a total surface area of 54 ${cm}^2$. The area occupied by a single red tile on Rubik's cube is

1. $0.25c{m}^2$

2. $0.5c{m}^2$

3. $1c{m}^2$

4. $2c{m}^2$

Q. A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.

Q. The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?

Q. A solid consists of a circular cylinder surmounted by a right circular cone. The height of the cone is h. If the total height of the solid is 3 times the volume of the cone, then the height of the cylinder is

(a) 2h

(b) $\frac{3h}{2}$

(c) $\frac{h}{2}$

(d) $\frac{2h}{2}$

Q.

Q. The total surface area of a cube of side a is ______.

1. $4a^2$
2. $6a^2$
3. $12a^2$
4. $3a^2$

Q.

The internal radii of the ends of a bucket, full of milk and of internal height 16 cm are 14 cm and 7 cm. If this milk is poured into a hemispherical vessel, the vessel is completely filled. The internal diameter of the hemispherical vessel would be

1. 30 cm

2. 10 cm

3. 20 cm

4. 28 cm

Q. Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.

Q. A metal cube is completely submerged in a cylindrical vessel containing water. The radius of the vessel is 5 cm, the level of water is raised by $\frac{140}{11}cm$. The volume of the cube is (in $c{m}^3$)

1. 100
2. 1000
3. 400
4. 27000

Q. If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?

Q.

A metallic cylinder has radius 3 cm & height 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled at the top-centre of the cylinder, and then completely filled with a lighter metal B. The conical hole has a radius of 1.5 cm & depth of ⁸/₉ cm. Calculate the ratio of volume of metal A to volume of metal B.

1. 11 : 3

2. 121 : 3

3. 133 : 2

4. 100 : 3

5. 121 : 2

Q.

The given figure shows a solid formed using a solid cube of side 40 cm and a solid cylinder of radius 20cm and height 50 cm attached to the cube as shown.

What is the total surface area of the whole solid [Take $\pi =3.14$] (Answer to the nearest integer)

1. 32533 $c{m}^3$

2. 52333 $c{m}^3$

3. 22533 $c{m}^3$

4. 25233 $c{m}^3$

Q.

Area of the base of a cone is 300 sq. cm and height is 15 cm. Find the volume of the cone.

Q. If a sheet measuring 1 m² costs ₹ 20, then the cost of the sheet required for making a cubical stand of edge 2.5 m, which is open from the top, is _______ .

1. ₹ 600
2. ₹ 625
3. ₹ 675
4. ₹ 655

Q.

The depth of a hemispherical water tank is 2.1 m at the centre. Find the capacity of the water tank in litres.

Q. A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm³ and its diameter is 7 cm, then find the height of the toy. [CBSE 2012]

Q.

A cone of maximum volume is carved out of a block of wood of size 20 cm x 10 cm x 10 cm. Find the volume of the cone carved out correct to 1 d.p. (π = 3.14)

1. 533.8 cm³

2. 523.3 cm³

3. 524.7 cm³

4. 573.5 cm³

5. 525.1 cm³

Q.

The picture below shows a petrol tank.

How many litres does it hold?

Q.

Which among the following will have the largest value?

1. Surface area of a cube with side $6\text{cm}$.

2. Surface area of a cuboid with $l=7\text{cm},b=6\text{cm}$ and $h=5\text{cm}$.

3. Surface area of the walls of a cube having side $8\text{cm}$.

4. Surface area of the walls of a cuboid having $l=10\text{cm},b=5\text{cm}$ and $h=6\text{cm}$.

Q.

A hemispherical depression is cut out from one face of a cubical block of side 7 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of remaining solid.

Q. Question 39(i)
A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded.
How many different scores are possible?

Q.

Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is

(a) 1 : 3 (b) 1 : 8 (c) 1: 9 (d) 1 : 18

Q.

Area of the base of a cone is 300 sq. cm and height is 15 cm. Find the volume of the cone.

Q.

The volume of a hemisphere is $2425\frac{1}{2}c{m}^3.$ Find its curved surface area.

Q. A building is in the form of a cylinder surrounded by a hemispherical dome. The base diameter of the dome is equal to $\frac{2}{3}$ of the total height of the building . Find the height of the building , if it contains $67\frac{1}{21}{m}^3$ of air.

Q.

Volume of a cone is 550 cm³ and diameter is 10 cm. Find the height of the cone.

Q.

Find the weight of a spherical shell of copper having external diameter $\mathbf{30}\mathbf{}\mathbf{cm}$ and thickness of $\mathbf{2}\mathbf{}\mathbf{cm}$. Density of copper is $\mathbf{10}\mathbf{}\mathbf{g}\mathbf{/}{\mathbf{cm}}^{\mathbf{3}}$.

Q.

The base-radius of a cylindrical block of wood is 15 centimetres and its height 40 centimetres. What is the volume of the largest cone that can be carved out from this?