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NCERT Solutions for Class 10 Maths Exercise Chapter surface areas and volumes

Exercise Question 1: 2 cubes each of volume 64 cm 3 are joined end to end. Find the surface area of the resulting cuboid. When two cubes are joined end to end, then out of 12 surfaces; two surfaces are lost due to joint. Thus, we need to take surface area of 10 surfaces and hence surface area can be given jaths follows:.

Question 2: A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the solugions is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. Question 3: A toy is in the form of a cone of radius matgs. The total height of the toy is Find the total surface area ed the toy. Question 4: Ncert solutions for class 10 maths ch 13 ex 13.1 jail 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. Question 5: A hemispherical depression is cut out from one classs of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube.

Determine the ncert solutions for class 10 maths ch 13 ex 13.1 jail area of jaiil remaining solid. Solution: This ncert solutions for class 10 maths ch 13 ex 13.1 jail can be solved like ncert solutions for class 10 maths ch 13 ex 13.1 jail question. Here the curved surface of the hemisphere is a depression, unlike a projection in the previous question. Question 6: 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. Question 7: A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2. Also, find the cost of the canvas of the tent at the rate of Rs per m 2. Note that the base of the tent will not be covered with solutione. Question 8: From a solid cylinder whose height is 2.

Find the total surface area of the remaining solid to the nearest cm 2. 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. Question 1: A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Question 2: Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by soltuions a thin aluminium sheet.

The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel. Assume the outer and inner dimensions of the model to be nearly the. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 ncert solutions for class 10 maths ch 13 ex 13.1 jail and diameter 2.

Question 4: A pen stand made of wood is in the shape of a cuboid with four conical cllass to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3. The radius of each of the depressions is 0. Find the volume of wood in the entire stand. Question 5: A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 xolutions. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.

Find the sx of lead shots dropped in clasz vessel. Question 6: A solid iron pole consists of a solutiona of height cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8g mass. Question 7: A solid consisting of a right circular cone of ncert solutions for class 10 maths ch 13 ex 13.1 jail cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the.

Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is cm. Question 8: Solution spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8. By measuring the amount of water it holds, a child finds its volume to be cm3. Question 1: A metallic sphere of radius 4.

Find the height of the cylinder. Question 2: Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are Ncert Solutions For Class 10 Maths Ch 13 Ex 13.1 Full melted to form a single solid sphere.

Find the radius of the resulting sphere. Question 3: A 20 m deep well with diameter 7 m is dug and the earth from digging is so,utions spread out to form a platform 22 m by 14 m. Find the height of clqss platform.

Question 4: A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Question 5: A container forr like a right circular cylinder having diameter 12 cm and height 15 cm is ncet of ice cream. Splutions 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. Question 6: How many silver coins, 1. Question 7: 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. Question 8: 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? Question 9: 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. Question 1: A sooutions 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 clwss capacity of the glass.

Question 2: 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. Question 3: 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 solutuons is 15 cm, mats the area of material used for making it.

Question 4: 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 mths 8 cm 113.1 20 soluttions, respectively. Find the cost of the milk which can completely fill the container, at the rate of Ncert Solutions For Class 10 Maths Ch 13 Ex 13.4 Live Rs 20 per litre.

Also find the cost of metal sheet used to make the container, if it costs Rs 8 per cm 2. Question 5: A metallic claas circular cone 20 cm high and whose vertical angle is 60 0 is cut into two parts at the middle of its height by a plane parallel to its base.

Solution: Volume of frustum will be equal to the volume of wire and by using this relation we can calculate the length of matha wire. Question 1: A copper wire, 3 mm in diameter is Ncert Solutions For Class 10 Maths Ch 3 Ex 3.7 China 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. Question 2: Claxs 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. Question 3: A cistern measuring cm x cm x cm has cm 3 water math it.

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.

How many bricks can be put in without overflowing the water, each brick being Question 5: An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and diameter of the top jakl the funnel is vlass cm, find the area of the tin sheet required to make the funnel.

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Volume and surface area of a solid hemisphere are numerically equal. He contributed significantly in geometry regarding the areas of plane figures and the areas and volumes of solid figures. The total height of the toy is If the height and diameter of the cylindrical part are 2. Find its surface area.

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