# Hemisphere and Its Surface Area

## Trending Questions

**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 dm2.

**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 242512 cm3. 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 cm2 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) 4πr2

(B) 6πr2

(C) 3πr2

(D) 8πr2

**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 7 cm.

- 308 cm2
- 318 cm2
- 388 cm2
- 368 cm2

**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 312 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

15 cm

18 cm

10 cm

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?

- 44π cm2
- 124π cm2
- 84π cm2
- 294π cm2

**Q.**Total surface area of a hemisphere with radius ′r′ units, will be equal to

- 4πr2
- 3πr2
- 43πr3
- 23πr3

**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 ______.

- 4πr2
- 6πr2
- 2πr2
- 12πr2

**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.

- 208 m2
- 358 m2
- 218 m2
- 308 m2

**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 242512cm3. 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

9000 cm

^{3}4400 cm

^{3}8800 cm

^{3}8000 cm

^{3}

**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?

- 100 %

- 300 %

- 50 %

- 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 π=227) [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 π=227)