Surface Area of Combined Figures

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.

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

Q.

A cone is of maximum size is carved out from a cube of edge $14cm.$ Find the surface area of the remaining solid after the cone is carved out.

Q.

From a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.

Q.

Two cubes each of volume 125 $c{m}^3$ are joined end to end to form a solid. Find the surface area of the resulting cuboid.

Q.

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. $[Take\pi =22/7.]$

Q.

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere.If the radius of the base of the cone is 21 cm and its volume is $\frac{2}{3}$ of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy? $(Use\pi =22/7)$

Q.

A vessel in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14cm$ and the total height of the vessel is $13cm$. Find the inner surface area of the vessel.

Q. From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. [CBSE 2014]

Q. From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use $\pi$ = 3.14)

Q.

A golf ball has a diameter equal to $4.2cm.$ Its surface has $200$ dimples each of radius $2mm.$ Assuming that the dimples are hemispherical, the total surface area which is exposed to the surroundings is

1. $85.82c{m}^2$

2. $90c{m}^2$

3. $100c{m}^2$

4. $80.58c{m}^2$

Q.

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

Q.

A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.

Q.

How many cubes of side 2 cm can be fit into a cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively?

Q. A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. Determine the surface area of the toy. (Use π = 3.14)

Q.

A circus tent is in the shape fo a cylinder surmounted by a conical top of same diameter.If their common diameter is 56 m, the height of the cylindrical part is 6m and the total height of the tent above the ground is 27m, find the area of the canvas used in making the tent.

Q.

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per $m^2$.

Q.

Question 8

$\Delta$ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of $\Delta$ ABC. What will be the height from C to AB i.e. CE?

Q. Two cubes each of volume 27 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid. [CBSE 2011, 14]

Q.

If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus respectively?

1. $1:1$

2. $3:4$

3. $1:1$

4. More than $1$

Q.

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready.

Q. A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs 2 per square metre, if the radius of the base is 14 metres.

Q.

A cone of height 8 metre has a curved surface area 188.4 square metres then its volume is what ?

Q.

Water is flowing at the rate of $6km/hr$ through a pipe of diameter $14cm$ into a rectangular tank which is 60 m long and $22m$ wide. Determine the time in which the level of water in the tank will rise by $7cm.$

Q. A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of the canvas use in making the tent, if the breadth of the canvas is 1.5 m.

Q.

A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it. [2 MARKS]

Q. A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/hr. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired ?

Q. Question 12
All the vertices of a rhombus lie on a circle . Find the area of the rhombus, if area of the circle is $1256c{m}^2$. (use $\pi =3.14$)

Q.

Water is being pumped out through a circular pipe whose diameter is 7 cm if the flow of water is 72 cm per second how many litres of water being pumped out in h our

Hope will get a relevant answer this time

Q.

The interior of a building is in the form of a right circular cylinder of diameter 4.2 m and height 4 m surmounted by a cone of same diameter. The height of the cone is 2.8 m. Find the outer surface area of the building.