Hemisphere and Its Surface Area

Q.

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solids is $104$ cm and the radius of each of the hemispherical ends is $7$ cm, find the cost of polishing its surface at the rate of Rs.$10$ per $d{m}^2$.

Q.

A semi-circular sheet of metal of diameter$28\mathrm{cm}$ is bent to form an open conical cup. Find the capacity of the cup.

Q.

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

Q.

The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 $c{m}^2$ of the surface is 10 paise.Find the total cost to paint the vessel all over.

Q. Question 15
If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is
(A) $4\pi r^2$
(B) $6\pi r^2$
(C) $3\pi r^2$
(D) $8\pi r^2$

Q. Question 3
In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Q.

Find the curved surface area of a hemisphere whose radius is $7cm$.

1. $308c{m}^2$
2. $318c{m}^2$
3. $388c{m}^2$
4. $368c{m}^2$

Q.

A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the hemisphere is equal to the edge of the cube.Determine the volume and total surface area of the remaining block.

Q.

A solid metal sphere is cut through its centre into 2 equal parts.If the diameter of the sphere is 3$\frac{1}{2}$ cm, find the total surface area of each part correct to two decimal places.

Q.

A plumbline (sahul) is the combination of

(a) a hemisphere and a cone

(b) a cylinder and a cone

(c) a cylinder and frustum of a cone

(d) a cylinder and a sphere

Q. In a corner of a rectangular field with dimensions $35\mathrm{m}\times 22\mathrm{m}$, a well with 14 m inside diameter is dug 8 m deep. The earth dug out is spread evenly over the remaining part of the field. Find the rise in the level of the field. [HOTS]

Q.

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then the height of the cone is

1. 15 cm

2. 18 cm

3. 10 cm

4. 24 cm

Q. The internal and external diameter of a hollow hemispherical shell are 6 cm and 10 cm respectively. What is the total surface area of the shell?

1. $44\pi c{m}^2$
2. $124\pi c{m}^2$
3. $84\pi c{m}^2$
4. $294\pi c{m}^2$

Q. Total surface area of a hemisphere with radius ${}^{\prime }{r}^{\prime }$ units, will be equal to

1. $4\pi r^2$
2. $3\pi r^2$
3. $\frac{4}{3}\pi r^3$
4. $\frac{2}{3}\pi r^3$

Q.

A solid sphere and a solid hemi-sphere have the same total surface area.Find the ratio between their volumes.

Q.

Question 5
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Q. If two solid hemispheres of same base radius r are joined together along their bases, then the curved surface area of this new solid is ______.

1. $4\pi r^2$
2. $6\pi r^2$
3. $2\pi r^2$
4. $12\pi r^2$

Q. The water for a factory is stored in a hemispherical tank, open at top, whose internal radius is 7 m. Find the interior surface area that needs to be painted.

1. 208 m${}^2$
2. 358 m${}^2$
3. 218 m${}^2$
4. 308 m${}^2$

Q.

A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.

Q.

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

Q. Question 1
A cylindrical pencil sharpened at one edge is the combination of
(A) a cone and a cylinder
(B) frustum of a cone and a cylinder
(C) a hemisphere and a cylinder
(D) two cylinders.

Q. Question 4
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Q.

The diameters of the top and bottom of a bucket are 40 cm and 20 cm respectively. If the depth of the bucket is 12 cm then its volume will be

1. 9000 cm³

2. 4400 cm³

3. 8800 cm³

4. 8000 cm³

Q.

Question 9
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Q. A plumbline (sahul) is a combination of


(a) a hemisphere and a cone
(b) a cylinder and a cone
(c) a cylinder and frustum of a cone
(d) a cylinder and a sphere

Q. What's the percentage change in the curved surface area of a hemisphere if the radius is doubled the initial radius?

1. 100 %
   
2. 300 %
   
3. 50 %
   
4. 150 %
   

Q.

The radius of a hemispherical balloon changes from $5cm$ to $15cm$. Find the ratio of the surface area of the balloon in the two cases.

Q.

The decorative block shown in Fig. 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 area of the block. (Take $\pi =\frac{22}{7}$) [2 MARKS]

Q. A sector is made into a hollow cone by bringing the radii together. If the radius of the cone is equal to its vertical height then the central angle of the sector is a) 45 root 2 b) 90 root 2 c) 180 root 2 d) 120 root 2

Q.

The decorative block shown in Fig. 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 area of the block. (Take $\pi =\frac{22}{7}$)