Surface Area of a Hemisphere

Q.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [4 MARKS]

Q.

Find the total surface area of hemisphere of radius 7 cm.(Take $\pi$ = $\frac{22}{7}$ )

1. 100$c{m}^2$

2. 364$c{m}^2$

3. 210$c{m}^2$

4. 462$c{m}^2$

Q.

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2 per square meter, find the volume of the air inside the dome.
$[Assume\pi =\frac{22}{7}]$

1. $223.9m^3$.

2. $123.9m^3$.

3. $523.9m^3$.

4. $525.9m^3$.

Q.

A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take $\pi =\frac{22}{7}$)

Q.

The radius of a hemisphere having the total surface area of 1848 cm${}^2$ is 7 cm.

1. True

2. False

Q.

The internal and external diameters of a hollow hemispherical vessel are 24cm and 25cm respectively. If the cost of painting $1c{m}^2$ surface area is$Rs.5.25$, find the total cost of painting the vessel all over. $\left(use\mathrm{\pi }=\frac{22}{7}\right)$

Q.

Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 3.5 cm.

Q.

A solid is hemispherical at the bottom and conical above. If the curved surface area of the two parts are equal, then what is the ratio of the height and radius of the conical part?

1. $\frac{1}{3}$

2. $\frac{\sqrt{3}}{1}$

3. $\frac{3}{1}$

4. $\frac{1}{\sqrt{3}}$

Q.

An inverted cone of vertical height 12$12cm$ and the radius of base $9cm$ contains water to a depth of $4cm$. Find the area of the interior surface of the cone not in contact with the water. [Use $\mathrm{\pi }=3.14$]

Q. With reference to the given figure. a metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and internal radius is 3.5 m. Calculate: [4 MARKS]
(i) The total area of the internal surface excluding the base
(ii) The internal volume of the container in $m^3$.
$(Use\pi =\frac{22}{7})$

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. If the length of each side of a cube measures a units, then its lateral surface area is square units and its total surface area is square units.

1. 4$a^2$
2. 6$a^2$
3. 3$a^2$
4. 9$a^2$

Q.

The curved surface area and the total surface area of a hemisphere of radius 7 cm will be

1. $308{cm}^2$ and $462{cm}^2$ respectively

2. $318{cm}^2$ and $480{cm}^2$ respectively

3. $310{cm}^2$ and $452{cm}^2$ respectively

4. $328{cm}^2$ and $562{cm}^2$ respectively

Q.

The total surface area of a solid sphere is 80 cm. It is split into two hemispheres. What is the surface area of the resulting hemisphere?

1. 20

2. 40

3. 80

4. 60

Q. The outer and inner diameters of a hemispherical bowl are 17 cm and 15 cm respectively. Find the cost of polishing it all over at 25 paise per $c{m}^2$. ( Take $\pi$ = $\frac{22}{7}$).

1. Rs. 260
2. Rs. 214.50
3. Rs. 240.50
4. Rs. 269

Q.

A hemispherical bowl is made of steel, 0.25 cm thick.The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. $[Assume\pi =\frac{22}{7}]$

1. $173.25c{m}^2$

2. $273.25c{m}^2$

3. $179.25c{m}^2$

4. $183.25c{m}^2$

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.

1. 20

2. 16

3. 18

4. 12

Q.

Assertion: The total surface area of a cone whose radius is $\frac{r}{2}$ and slant height $2l$ is $\left(\pi \right)r\left(l+\frac{r}{4}\right)$.

Reason: Total surface area of cone is $\pi r(l+r)$ where $r$ is radius and $l$ is the slant height of the cone.

Which of the following is correct?

1. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3. If Assertion is correct but Reason is incorrect.

4. If Assertion is incorrect but Reason is correct.

Q.

A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

1. $=Rs.11.55$

2. $=Rs.21.55$

3. $=Rs.31.55$

4. $=Rs.17.55$

Q.

An iron spherical ball of radius 21cm is melted and re-casted into hemispheres of radius 7cm. The number of balls formed will be

___

Q. A hemisphere of radius 21 cm, made up of iron is melted and moulded to form a cone of height 21 cm. What is the ratio of the curved surface area of the hemisphere to that of the cone?

1. $2\sqrt{2}:3$
2. $\sqrt{3}:\sqrt{2}$
3. $2\sqrt{3}:\sqrt{5}$
4. $1:2$

Q.

The radius of a hemisphere having total surface area of $1848$ sq. cm is $7cm$

1. False

2. True

Q. A hemispherical bowl is made of brass, $7cm$ thickness. The inner radius of the bowl is $7cm$. Find the ratio of outer surface area to inner surface area.

1. $1:4$
2. $2:1$
3. $1:2$
4. $4:1$

Q. A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid for the bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

Q. A hemispherical bowl of radius unity is filled up with water upto the depth $\frac{1}{2}$. The volume of water in the bowl is

1. $\frac{5\pi }{24}$
2. $\frac{27\pi }{24}$
3. $\frac{3\pi }{4}$
4. None of these

Q.

A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid for the bowl. Tin plating is done at the rate of ₹10 per 100 sq.cm.

1. ₹ 115.5

2. ₹ 11.55

3. ₹ 1.155

4. ₹ 1155

Q.

An iron spherical ball of radius 21cm is melted and it is re-casted in hemispheres of radius 7cm. The number of balls formed is ___.

Q. Find the total surface area of a hemisphere of radius $10$ cm. (Use $\pi =3.14$)

1. $942{cm}^2$
2. $492c{m}^2$
3. $924c{m}^2$
4. $249c{m}^2$

Q.

The Height Of A Cone Is$16cm$ And Its Base Radius Is $12cm$ $(\mathrm{\pi }=3.14)$. Find Its Curved Surface Area.

Q.

A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of Rs.10 per 100 sq.cm. [4 MARKS]