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Find the height of the embankment. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Let the height and radius of ice cream container cylinder be h1 and r1. How many silver coins, 1. We know that, every coin has a shape of cylinder. Let radius and height of the coin are r1 and h1 respectively. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Let the radius and slant height of the heap of sand are r and l. Water in a canal, 6 m wide and 1. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed? A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. The slant height of a frustum of a cone is 4 cm and the perimeters circumference of its circular ends are 18 cm and 6 cm.
Find the curved surface area of the frustum. Let the slant height of the frustum be l and radius of the both ends of the frustum be r1 and r2. A fez, the cap used by the turks, is shaped like the frustum of a cone see figure. 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. Let the slant height of fez be l and the radius of upper end which is closed be r1 and the other end which is open be r2.
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Also find the cost of metal sheet used to make the container. Let h be the height of the container, which is in the form of a frustum of a cone whose lower end is closed and upper end is opened. Also, let the radius of its lower end be r1 and upper end be r2.
Let r1 and r2 be the radii of the frustum of upper and lower ends cut by a plane. A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm and diameter 10 cm, so as to cover the curved surface of the cylinder.
Find the length and mass of the wire, assuming the density of copper to be 8. When a wire is one round wound about a cylinder, it covers a 3 mm of length of the cylinder. A right triangle, whose sides are 3 cm and 4 cm other than hypotenuse is made to revolve about its hypotenuse.
Find the volume and surface area of the double cone so formed. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. In one fortnight of a given month, there was a rainfall of 10 cm in a river valley.
If the area of the valley is km 2 , show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each km long, 75 m wide and 3 m deep. Write your views on recycling of water. The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height.
Find the ratio of the volumes of the two parts. To solve some problems related to daily life situations involving surface areas and volumes of above solid figures. For solving above type of problems, we need to find the perimeters and areas of simple closed plane figures figure which lie in a plane and surface areas and volumes of solid figures figures which do not lie wholly in a plane.
You are already familiar with the concepts of perimeters, areas, surface areas and volumes. We come across multiple objects in our daily lives that are a combination of many of these shapes. For example, a truck carrying oil which is in the shape of a cylinder that has 2 hemispheres at its end. In the Surface Area Volume Class 10 you would learn how to calculate the surface area and volumes of such solids which are a combination of two or more solid shapes.
The outer part of any 3-D figure is the surface area of that figure. To find out the surface area of a solid which is a combination of solid shapes, we would need to find out the surface area of individual solid shapes separately to find the surface area of the entire 3-D solid shape. Let us clarify this with an example:.
The solid in the figure above is a combination of a cone, cylinder, and hemisphere. The volume of solids by joining two or more basic solids is the sum of the volumes of individual solids. Let us understand this with an example:. The solid in the above figure is made up of two solids, i. So the total volume of the solid is obtained by adding up the volume of these two constituent solids.
When we convert a solid from one form to another by the method of melting or remoulding, then the volume of the solid stays the same, despite the change in shape.
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