13. Surface Areas and Volumes

Surface Areas and Volumes

Chapter 13. Surface Areas and Volumes

Class 10 Maths Chapter 12 Areas Related to Circles : Multiple Choice Questions , Answer following the Questions , Fill in the blanks , 2 Marks Questions , 3 Marks Question, 4 Marks Question and Solutions :

Class 10 Surface Areas and Volumes Multiple Questions and Solution:

SECTION = A

Q1. 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 ]

Q2. 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 ,

]

Q3. 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

]

Q4. 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)

Q5. 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 ,

]

Q4. 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

]

Q5. 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 , cm and cm

A/Q ,

Therefore , the diameter cm ]

Q4. 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

]

Q6. 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 ]

Q11. 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 ,

]

Q7. If be the height , be the slant height and and are the radii of the ends of the frustum of a cone , then the volume of the frustum of the cone is :

(a) (b)

Solution: (b)

Q8. 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 cm ,

the radius of cylinder cm and cm

The number of solid spheres

]

Q9. 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 ,

cm ]

Class 10 Surface Areas and Volumes Fill in the blank :

Q1. If a sphere of the radius 7 cm , then the surface area of a sphere is .

Solution: 616 cm2 .

[ Here , cm

The surface area of the sphere

]

Q2. The volume and surface area of a sphere are equal , then the diameter of the sphere is ( 3 units / 6 units / 2 units / 4 units) [SEBA 17]

Solution: 3

[ A/Q ,

units ]

Q3. 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 .

Solution: 6 cm

[ Here , cm , cm and cm

let be the edge of new cube .

A/Q ,

cm ]

Q4. The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is .

Solution: .

[ Here , cm and cm

The volume of the largest right circular cone

]

Class 10 Surface Areas and Volumes Answers following the questions :

Q1. 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

Q2. 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 .

Q3. Two identical cubes each of volume 125 are joined together end to end ,then find the surface area of the resulting cuboid .

Solution: Given ,

Here , cm , cm and

Therefore, the surface area of the resulting cuboid

Q4. 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 .

Q5. 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

Q6. 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

Q7. 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 , cm and cm

Therefore, the number of spherical bullets

Class 10 Surface Areas and Volumes 2 Marks Questions and Solutions

SECTION = B

Q1. 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

Class 10 Surface Areas and Volumes 3 Marks Questions and Solutions

SECTION = C

Q1. A hemispherical tank full of water is emptied by a pipe at the rate of litres per second .How much time will it take to empty half the tank , if it is 3 m in diameter ? [ Take = 22/7]

Solution: For hemispherical tank :

Here , Diameter m ; Radius m

The volume of hemispherical tank

So, the volume of the water to be emptied

litres

Since, litres of water is emptied in 1 second .

litres of water is emptied in

second

. minutes .

Class 10 Surface Areas and Volumes 4 Marks Questions and Solutions

SECTION = D

Q1. 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