Chapter 13: Surface Areas and Volumes– Chapter-Wise Important Questions and Answers | Class 10 Mathematics CBSE Solutions

CBSE Class 10 Mathematics Chapter 13: Surface Areas and Volumes Important Questions with Solutions and Answers

Chapter 13: Surface Areas and Volumes

SECTION = A

Question: The volume of a sphere is . The radius of the sphere is : [SEBA 2019]

(a) 2 cm (c) 4 cm (c) 6 cm (d) 8

Solution: (c) 6 cm

[ Let be the radius of the sphere .

A/Q , cm ]

Question: The volume of two spheres are in the ratio then the ratio of their surface areas is : [SEBA16]

(a) 1 : 2 (b) 2 : 3 (c) 9 : 16 (d) 16 : 9

Solution: (d) 16 : 9

[ A/Q ,

]

Question: A cuboid whose length , breadth and height are 15 cm , 10 cm and 20 cm respectively ,then its surface area is :

(a) 1200 (b) 1400 (c) 1300 (d) 3000

Solution: (c) 1300 .

[ Here, cm , cm and cm

The surface area cuboid ]

Question: If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is :

(a) (b) (c) (d)

Solution: (a)

Question: If the radius of the bases of two right circular solid cones of same height are and respectively . The two cones melted and recast into a solid sphere of radius,then height of the cone is :

(a) (b) (c) (d)

Solution: (c)

[ A/Q ,

]

Question: Two identical cubes each of volume are joined together end to end ,then the surface area of the resulting cuboid is : [SEBA 2018 , 20]

(a) (b) (c) (d)

Solution: [ Given ,

Here , cm , cm and cm

Therefore, the surface area of the resulting cuboid ]

Question: Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm . The diameter of each sphere is :

(a) 4 cm (b) 3 cm (c) 2 cm (d) 6 cm

Solution: (c) 2 cm

[ Let be the radius of the sphere .

Here , and cm

A/Q ,

Therefore , the diameter cm ]

Question: In the given figure, if and are radius and height of cylinder, then the total curve surface area of the cylinder is :

(a) (b) (c) (d)

Solution: (d) .

[ The total CSA of cylinder ]

Question: Three metallic spheres of radii 6 cm , 8 cm and 10 cm respectively are melted to form a single solid sphere . The radius of the resulting sphere is :

(a) 12 cm (b) 24 cm (c) 48 cm (d) 480 cm

Solution: (a) 12 cm

[ Let be the radius of the sphere .

Hare, cm , cm and cm

A/Q ,

cm ]

Question: If be the height of the two same right circular cone and their base radius are and respectively . The cones are melted and recast into a cylinder of same height , then the radius of the cylinder is :

(a) (b) (c) (d)

Solution: (d)

[ A/Q ,

]

Question: The number of solid spheres, each of diameter 6 cm than can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is : [CBSE 2014 ]

(a) 3 (b) 5 (c) 4 (d) 6

Solution: (b) 5

[ Here, The radius of sphere , the radius of cylinder and cm

The number of solid spheres ]

Question: A rectangular sheet of paper 40 cm × 22 cm , is rolled to form a hollow cylinder of height 40 cm . The radius of the cylinder (in cm) is : [CBSE 2014 F]

(a) 3.5 (b) 7 (c) 8 (d) 5

Solution: (a) 3.5

[ Here, cm , cm and cm

Area of rectangular sheet of paper

A/Q ,

]

Question: If a sphere of the radius 7 cm , then the surface area of a sphere is :

(a) 661 cm² (b) 616 cm² (c) 646 cm² (d) 88 cm²

Solution: (b) 616 cm² .

[ Here , cm

The surface area of the sphere ]

Question: The volume and surface area of a sphere are equal , then the diameter of the sphere is : [SEBA 2017]

(a) 3 units (b) 6 units (c) 2 units (d) 4 units

Solution: (a) 3 units

[ A/Q ,

units ]

Question: Three metallic solid cubes whose edges are 3 cm , 4 cm and 5 cm are melted and formed into a single cube , then the edge of the new cube is :

(a) 10 cm (b) 8 cm (c) 6 cm (d) 11 cm

Solution: (c) 6 cm

[ Here , cm , cm and cm

let be the edge of new cube .

A/Q , cm ]

Question: The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is :

(a) 17.50 cm³ (b) 20.207 cm³ (c) 19.404 cm³ (d) 18.503 cm³

Solution: (c) .

[ Here , cm and

The volume of the largest right circular cone ]

Answers Following the Questions

Question: 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 , then find the volume of the solid in terms of .

Solution: Here , cm

The volume of the solid

Question: A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm . Find the height of the cylinder .

Solution: Let be the height of the cylinder .

Here , cm and cm

A/Q ,

Therefore, the height of the cylinder is 2.744 cm .

Question: Two identical cubes each of volume 125 are joined together end to end ,then find the surface area of the resulting cuboid .

Solution: Given , cm

Here , cm , cm and

Therefore, the surface area of the resulting cuboid

Question: The surface area of a sphere is 616 . Find its radius .

Solution: Let , be the radius of the sphere .

A/Q ,

Therefore, the radius is 7 cm .

Question: How many balls , each of radius 2 cm , can be made from a solid sphere of lead of radius 8 cm ?

Solution: Here , cm and cm

Therefore, number of the balls

Question: The volume and surface area of a solid hemisphere are numerically equal .What is the diameter of hemisphere ? [2017 Delhi]

Solution: let be the radius of the hemisphere .

A/Q ,

Therefore, the diameter of the hemisphere cm

Question: How many spherical bullets each of 6 cm in diameter can be cast from a rectangular block of metal 44 cm × 15 cm × 10 cm ?

Solution: Here , Radius , cm , cm and cm

Therefore, the number of spherical bullets

SECTION = B

Question: A 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 .

Solution: The cubical block of side is 7 cm .

So, the greatest diameter of the hemisphere is 7 cm .

Here , Radius ,

The surface area of the solid Area of cubical block + Area of hemisphere – Area of circular top

Question: If the total surface area of a solid hemisphere is , find its volume . [ Take ] [CBSE 2014]

Solution: Let be the radius of the hemisphere .

A/Q ,

Therefore, the volume of hemisphere

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

Solution: Here, Radius

The height of the cylinder

Area of the inner surface of the vessel Area of cylinder + Area of hemisphere

SECTION = C

Question: From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out . Find the total surface area of the remaining solid to the nearest .

Solution: Here , Diameter, Radius , Height

The slant height

The total surface area of the remaining solid C.S.A of cylinder + C.S.A. of cone + Area of circular top

[approx.]

Question: A spherical glass vessel has a cylindrical neck 8 cm long , 2 cm in diameter ; the diameter of the spherical part is 8.5 cm . By measuring the amount of water it holds , a child find its volume to be 345 . Check whether she is correct , taking the above as the inside measurements, and .

Solution: For cylindrical neck : Here ,

The volume of cylindrical neck

For spherical part : Here , ,

The volume of spherical part

The volume of spherical glass vessel

She is not correct . The correct answer is .

Question: 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 .

Solution: For cone : Radius ,

Height cm

The slant height 12.5 cm

The curve surface area of cone

For hemisphere : Radius

The curve surface area of hemisphere

The total surface area of the toy .

Question: A tent is in the shape of a cylinder surmounted by a conical top . If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent . Also, find the cost of the canvas of the tent at the rate of Rs 500 per . (Note that the base of the tent will not be covered with canvas)

Solution: Here , Height , Diameter , Radius and the slant height

The area of the canvas of the tent Area of the cylinder + C.S. area of cone

The cost of the canvas of the tent .

Question: A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11 . 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 .

Solution: Here , Radius Height

The total surface area of the article C.S.A. of cylinder + Area of 2 hemisphere

SECTION = D

Question: A gulab jamun, contains sugar syrup up to about 30% of its volume . Find approximately how much syrup would be found in 45 gulab jamuns , each shaped liked a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see Fig. 13.15)

Solution: Here, , and

The volume of a gulab jamuns = The volume of the hemisphere + The volume of the cylinder + The volume of the hemisphere

The volume of 45 gulap jamuns

The volume of gulap jamun contains in sugar syrup

Question: 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.

Solution: For cylinder : Diameter cm , Radius cm and Height cm

The volume of cylinder

For cone : Height cm , Diameter cm and Radius cm

The total volume hemispherical shape of cone The volume of cone The volume of hemisphere

The total number of such cones which can be filled with ice cream

Question: A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens . The dimensions of the cuboid are 15cm by 10cm by 3.5 cm . The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm . Find the volume of wood in the entire stand (see Fig. 13.16) .

Solution: For cuboid : Here , length cm , breadth cm , height cm

The volume of a cuboidal wood

For cone : Here , and

The volume of a cone

The volume of 4 cone

Therefore, the volume of wood in the entire stand

Question: 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 cm . It is filled with water up to the brim . When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel , one-fourth of the water flows out . Find the number of lead shots dropped in the vessel .

Solution: For cone : Here, Height cm and Radius cm

The volume of cone

For Sphere : Here, Radius cm

The volume of the sphere

The volume of the water that flows out of the cone (the volume of the cone)

Therefore, the number of lead shots

Question: A solid consisting of a right circular cone of height 120 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 bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is 60 cm and its height is 180 cm .

Solution: For cone and hemisphere : Here, Radius and Height

The volume of solid The volume of cone + The volume of hemisphere

For Cylinder : Here , Radius and Height

The volume of Cylinder

The volume of water left in the cylinder Volume of Cylinder – Volume of solid

Posted 5 years ago

Chapter 13: Surface Areas and Volumes– Chapter-Wise Important Questions and Answers | Class 10 Mathematics CBSE Solutions

CBSE Class 10 Mathematics Chapter 13: Surface Areas and Volumes Important Questions with Solutions and Answers

Chapter 13: Surface Areas and Volumes

Answers Following the Questions

SECTION = B

SECTION = C

SECTION = D

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