Cone

Q.

Question 9
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

Q. The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface. (in $m^2$)

1. $30\pi$
2. $40\pi$
3. $60\pi$
4. $80\pi$

Q.

In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

1. 24π cm

2. 52π cm

3. 26π cm

4. 72π cm

Q. A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. The surface area of the toy is _____ (Use $\pi =3.14$)

1. $47.1c{m}^2$
2. $103.62c{m}^2$
3. $160.14c{m}^2$
4. $56.52c{m}^2$

Q. Question 5
The shape of a gilli, in the gilli-danda game ( see – figure) is a combination of

(A) two cylinders
(B) a cone and a cylinder
(C) two cones and a cylinder
(D) two cylinders and a cone

Q.

A vessel is in the shape of a cube of side 30 $m$. How much water can it hold?

1. 27000 $m^3$
2. 26000 $m^3$
3. 28000 $m^3$
4. 29000 $m^3$

Q.

The height and radius of cone are $4cm$ and $3cm$ respectively. Find the curved surface area of cone.

1. $14\pi {cm}^2$

2. $15\pi {cm}^2$

3. $12\pi {cm}^2$

4. $16\pi {cm}^2$

Q.

Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see Fig). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take $\pi =\frac{22}{7}$) [4 MARKS]

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.

Q. A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required in $m^2$?

1. 463.39

Q.

A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed.

___

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.

Q. If the area of base of a cone is 49$\pi m^2$ and its CSA is 175$\pi m^2$, then its height is .

1. 34 m
2. 25 m
3. 24 m

Q. A toy is a combination of a cylinder, hemisphere and a cone, each with radius $10cm$ as shown in the figure. Height of the conical part is $10cm$ and total height is $60cm$. Find the total surface area of the toy $(\pi =3.14,\sqrt{2}=1.41)$.

1. $4382.74c{m}^2$
2. $3582.74c{m}^2$
3. $4882.74c{m}^2$
4. $35982.74c{m}^2$

Q.

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

1. 262.39 $m^2$

2. 463.39 $m^2$

3. 662.39 $m^2$

4. 563 $m^2$

Q.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.
$(Use\pi =\frac{22}{7})$

1. $400{cm}^2$

2. $267{cm}^2$

3. $258{cm}^2$

4. $374{cm}^2$

Q.

A toy has a hemispherical base with a conical top attached to it. Radius of the hemisphere = 6 cm. Height of the cone = 8 cm. What is the surface area of the toy?

1. 132$\pi$ $c{m}^2$

2. 100$\pi$ $c{m}^2$

3. 82$\pi$ $c{m}^2$

4. 60$\pi$ $c{m}^2$

Q. Curved surface area of a cone with base radius $40$ cm is $1640\pi$ sq. cm. Find the height of the cone in cm.

Q. A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75cm.The radius of base of cone.

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 is $15.5$ cm. Find the total surface area of the toy.

1. $234.5c{m}^2$
2. $224.5c{m}^2$
3. $214.5c{m}^2$
4. $204.5c{m}^2$