Surface Areas and Volumes Class 10 Important Questions | NCERT Maths Chapter-13

Surface Areas and Volumes Class 10 Important Questions

The start of class 10 marks the beginning of the foundation for class 11 and class 12. It is very important study the basics in order to understand each and every chapter properly. In this page, we have provided all the important question for cbse class 9 that could be asked in the examination. Students also need to study the ncert solutions for class 10 in order to gain more knowledge and understanding the lessons. Questions and Answers are way to learn the new things in a proper way. NCERT textbooks downloads for class 9 in pdf are also available for the students if they need more help. By downloading these books, they can study from it. Our experts also prepared revision notes for class 9 so that students should see the details of each and every chapters. Class 9 important questions are the best to revise all the chapters in the best way.

Question 1.
In Figure, a decorative block, made up of two solids a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has a diameter of 3.5 cm. Find the total surface area of the block.(use π=22/7)

Solution:
Side of the cube = 6 cm

Question 2.
A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment
Solution:

Question 3.
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder, (use π=22/7)
Solution:

Question 4.
A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone, (use π = 3.14)
Solution:

Question 5.
A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy(use π =22/7)
Solution:

Question 6.
In figure, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at therate of rupees 500/sq. metre. (use π=22/7)

Solution:

Question 7.
A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel
Solution:

Question 8.
A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3×5/9 cm. Find the diameter of the cylindrical vessel
Solution:

Question 9.
A hemispherical tank, of diameter 3 m, is full of water. It is being emptied by a pipe 3×4/7 litre per second. How much time will it take to make the tank half empty?
Solution:

Question 10.
A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone.
Solution:

Question 11.
A metal container, open from the top, is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper circular ends are as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at of rupees 35/litre
Solution:

=1/3 x 22/7 x 21[400+64+160]=22 x 624/1000 liters[1 cm³=1/1000 l]
cost of 1l milk=35rupees
cost of milk in container=35  22 x 624/1000=480.48 rupees

Long Answer Type Questions [4 Marks]

Question 12.
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm³. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket, (use π=3.14)
Solution:
Let R, r and V be the upper radius, lower radius and volume of the frustum respectively then
R = 20 cm, r = 12 cm and V = 12508.8 cm³

12308.8 = 1/3x 3.14 [400 + 144 +240]h
h=12308.8 x 3/3.14 x 784 h=15 cm
Now, l (slant height) =√(20-12)²+15²=√64+225=√289=17 cm²
Total area of the metal sheet=curved surface area of the cone+area of the base=  π(R+r)l+πr²
=π(20+12)x 17+π x 12 x 12
=π x 32 x 17 +144π =688π
=688 x 3.14 =2160.32 cm²

Question 13.
The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle
Solution:

Question 14.
Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs ? 120 per sq.m, find the amount shared by each school to set up the tents.What value is genetated by above problem?
Solution:

Question 15.
In figure, shown a right circular cone of height 30 cm. A small cone is cut off from the top by a plane parallel to the base. If the volume of the small cone is 1/27 of the volume of given cone, find at what height above the base is the section made.

Solution:

Important Links

NCERT Quick Revision Notes- Surface Areas and Volumes

NCERT Solution- Surface Areas and Volumes

Important MCQs- Surface Areas and Volumes

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