Surface Area of Combination of Solids

Q.

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, then its total surface area is

1. 220.6 cm²

2. 214.5 cm²

3. 216.2 cm²

4. 212.6 cm²

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

Q.

A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. The total surface area of the toy will be

1. 400 cm²

2. 304 .5 cm²

3. 231 cm²

4. 203.94 cm²

Q. In the given figure, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy.

Q.

From a solid right circular cylinder of height $2.4cm$ and radius $0.7cm$ a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.

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 solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm² .

Q. In the given figure shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and surface area of the toy from the measures shown in the figure ($\mathrm{\pi }=3.14$)

Q.

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.

Q. Question 3
Write ‘True’ or ‘False’ and justify your answer in the following.

A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is $\pi r\sqrt{r^2+h^2}+3r+2h$

Q. A hemisphere the diameter of whose base is equal to the side of a cube is placed upon the upper face of the cube if the side of the cube is 14 cm find the total surface area of the solid combination

Q. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm find the total surface area and volume of the toy.

Q. Choose the correct answer of the following question:

A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is

(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1 [CBSE 2011]

Q.

A hemispherical piece of wood is to be mounted at the end of a cylindrical wooden log with the same base.

If the length of the log is four times its width, then what is the percentage increase in its total surface area?

1. 

2. 

3. 

4. 

Q.

A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

Q. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical end is 7 cm, find the surface area of the solid.

Q. A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.

Q. A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m, respectively, and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required.

Q. A gift containing cylinder surmounted by cone is to be wrapped. What is the surface area to be wrapped if the cylinder of 10 cm height and 3.5 cm radius and cone has slant height of 7 cm ?

1. $235.5{\text{cm}}^2$
2. $200.5{\text{cm}}^2$
3. $335.5{\text{cm}}^2$
4. $300.5{\text{cm}}^2$

Q. What is the curved surface area of a cone filled with cream forming a hemishpere on top?

1. πrl+πr
2. πl+πr
3. πrl+πr
4. πrl+2πr²

Q. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid 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. 15. Monica has a piece of canvas whose area is 818 metres square . She uses it to have a conical tent made with the base radius of 10 metre. Assuming that all the stitching margins and the wastage incurred while cutting amounts to approximately 1.6 metres square .Find the volume of the tank that can be made with it. Click here to view details:

Q. 1. What lenght of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra lenght of material that will be required for stitching margins and wastage in cutting is approximately 20 cm ( use pie= 3.14).

Q. The surface area of the solid of hemispherical base of radius 7 cm surmounted by cone of slant height 7 cm is ____.

1. 221 cm${}^2$
2. 462 cm${}^2$
3. 262 cm${}^2$
4. 421 cm${}^2$

Q. With a cylindrical bucket of radius 14 cm and height 16 cm, 27 buckets of lime was poured to form a conical heap. If the area of its base is 5544 cm, then the canvas required to cover it will be

Q.

A 15 cm tall cylindrical bucket of base diameter 6 cm, is recast to form a frustum with radii 2 cm and 4 cm. Find the height of the frustum obtained.

1. 11.75 cm

2. 14.47 cm

3. 13.21 cm

4. 12.52 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. Determine the surface area of the toy. (Use π = 3.14)

Q. Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
(3 Marks)

Q. A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent.
(Take : π = 22/7)

Q. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.