KSEEB Solutions for Class 10 Maths Chapter 15 Surface Areas and Volumes Additional Questions

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Karnataka State Syllabus Class 10 Maths Chapter 15 Surface Areas and Volumes Additional Questions

I. Multiple Choice Questions:

Question 1.
A cylindrical pencil sharpened at one edge is the combination of
a. cone and cylinder
b. Frustum of a cone and cylinder
c. A hemisphere and a cylinder
d. two cylinders
Answer:
a. cone and cylinder

Question 2.
The curved surface area of a solid hemisphere of radius r is
a. 4πr²
b. 2πr²
c. 4/3πr³
d. 3πr²
Answer:
b. 2πr²

Question 3.
A shuttlecock used for playing badminton has the shape of a combination of
a. a cone and a sphere
b. frustum of a cone and a hemisphere
c. a cylinder and a hemisphere
d. a cone and a cylinder
Answer:
b. frustum of a cone and a hemisphere

Question 4.
The ratio of the radii of two spheres is 4 : 5. Find the ratio of their total surface areas is.
a. 5 : 4
b. 4 : 5
c. 16 : 25
d. 25 : 16
Answer:
c. 16 : 25

Question 5.
If the volume of a cube is 1331 cm³ the length of its edge is equal to
a. 12
b. 11
c. 15
d. 13
Answer:
b. 11

Question 6.
If the diameter of a sphere is d, then its volume is
a. \(\frac{1}{3}\)πd³
b. \(\frac{1}{24}\)πd³
c. \(\frac{4}{3}\)πd³
d. \(\frac{1}{6}\)πd³
Answer:
d. \(\frac{1}{6}\)πd³

Question 7.
The ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube is
a. 6 : π
b. 4 : π
c. 2 : π
d. 3 : π
Answer:
a. 6 : π

Question 8.
A cylinder, a cone and hemisphere are of equal base and have the same height the ratio of their volumes is
a. 3 : 2 : 1
b. 2 : 3 : 1
c. 3 : 1 : 2
d. 1 : 2 : 3
Answer:
c. 3 : 1 : 2

Question 9.
A solid sphere of radius r is melted and cast into the shape of a solid cone of height r. The radius of the base of the cone is.
a. r
b. 3r
c. 4r
d. 2r
Answer:
d. 2r

Question 10.
If a rectangle revolves about one of its sides and completes a full rotation the solid formed is called
a. sphere
b. cylinder
c. hemisphere
d. cone
Answer:
b. cylinder

Question 11.
A hollow cylinder has only
a. curved surface area
b. total surface area
c. volume
d. Perimeter
Answer:
a. curved surface area

Question 12.
The formula to find the volume of the cylinder.
a. πr²h
b. 2πr²h
c. 2πr(r + l).
d. πrl
Answer:
a. πr²h

Question 13.
Is a circular disc is rotated about one of its diameters the solid thus generated is called
a. cylinder
b. sphere
c. cone
d. frustum
Answer:
b. sphere

Question 14.
The surface area of a sphere is
a. 4πr²
b. 4πr³
c. πrl
d. 2πr (r + 1).
Answer:
a. 4πr²

Question 15.
The CSA of sphere is
a. 4πr²
b. 3πr²
c. 2πr²
d. πr²
Answer:
a. 4πr²

Question 16.
The surface areas of two sphere are in the ratio 1 : 4 then the ratio of their volumes is
a. 1 : 4
b. 1 : 8
c. 1 : 16
d. 1 : 64
Answer:
b. 1 : 8

Question 17.
The base radii if two circular cones of the same height are in the ratio 3:5. Find the ratio of their volumes.
a. 3 : 5
b. 5 : 3
c. 9 : 25
d. 27: 125
Answer:
c. 9 : 25

Question 18.
The volume of a cone of height 4 cm is 168π cm³ the radius of the cone is
a. 6 cm
b. 8 cm
c. 10 cm
d. 12 cm
Answer:
a. 6 cm

Question 19.
How many lead balls of radius 2 cm can be made from a ball of radius 4 cm
a. 1
b. 2
c. 4
d. 8
Answer:
d. 8

Question 20.
The volume of a frustum of a cone of height h and ends radii r₁ and r₂ is.

Answer:

Question 21.
If the diameter of a sphere is ‘d’ then its volume is
a. \(\frac{1}{3}\)πd³
b. \(\frac{1}{2}\)πd³
c. \(\frac{4}{3}\)πd³
d. \(\frac{1}{6}\)πd³
Answer:
d. \(\frac{1}{6}\)πd³

Question 22.
The internal and external radii of a hemispherical bowl are r₁ and r₂ respectively the surface area of the bowl is

Answer:

Question 23.
The formula to find the slant height of the cone.

Answer:
b. l = \(\sqrt{h^{2}+r^{2}}\)

II. Short Answer Questions:

Question 1.
Two identical solid hemispheres of equal base radius r cm are struck together along their bases. What will be the total surface area of the combination.
Answer:
The resultant solid will be a sphere of radius r whose total surface area is 4πr².

Question 2.
A solid ball is exactly fitted inside the cubical box of side a. What is the volume of the ball?
Answer:
Diameter of ball = edge of cube = a
∴ r = \(\frac{a}{2}\)
Volume of a ball

Question 3.
The radii of the ends of a frustum of a cone 40 cm high are 20 cm and 11 cm. Find its slant height.
Answer:

Question 4.
A solid piece of iron in the form of a cuboid of dimension 49 cm × 33 cm × 24 cm is melted to form a solid sphere. Find the radius of sphere.
Answer:
49 × 33 × 24 = 4/3 πr³

r = 21 cm

Question 5.
Write the formula to find lateral surface area of frustum of cone.
Answer:
LSA = πl(R + r).

Question 6.
Write the formula to find volume of spherical shell.
Answer:
Volume of spherical shell = 4/3 π(R³ – r³).

Question 7.
If two cubes of edge 5 cm each are joined end to end, find the surface area of the resulting cuboid.
Answer:
total length = (l) = 5 + 5 = 10 cm
Breadth = b = 5 cm and
height = h = 5 cm
Surface area = 2 (lb + bh + lh)
= 2 (10 × 5 + 5 × 5 + 5 × 10)
= 2 × 125
= 250 cm²

Question 8.
What is the ratio of the volume of a cube to that of a sphere which will fit inside it.
Answer:
Let edge of the cube be ‘a’
diameter of the sphere will fit inside the given cube = a
∴ volume of the cube : volume of the sphere

Question 9.
Write the formula to find slant height of an frustum cone.
Answer:

III. Long Answer Questions:

Question 1.
A solid hemisphere of wax of radius 12 cm is melted and made into a cone of base radius 6 cm. Calculate the height of the cone.
Answer:
Radius of the hemisphere, r₁ = 12 cm
Radius of the base of the cone, r₂ = 6 cm.
Height of the cone = h = ?
volume of wax cone = volume of wax hemisphere.

Question 2.
21 spheres of equal radii are melted to form a cylinder of radius 14 cm and height 49 cm. Find the radius of sphere.
Answer:
radius of cylinder = r₁ = 14 cm
height h = 49 cm and radius of sphere = r₂
Total volume of 21 spheres = volume of cylinder.

∴ radius of the sphere is 7 cm.

Question 3.
A hemispherical bowl of internal radius 9 cm is full of with a liquid, this liquid is to be filled into cylindrical shaped bottles of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?
hemisphere r₁ = 9 cm
Cylinder r₂ = \(\frac{d}{2}=\frac{3}{2}\) cm and h = 4cm
Number of bottles

Question 4.
A bucket is in the shape of a frustum with the top and bottom circles of radii 15 cm and 10 cm. Its depth is 12 cm. Find its curved surface area and total surface area. (Express the answer in terms of π).
Answer:
r₁ = 15 cm, r₂ = 10 cm and h = 12 cm

l = 13cm
CSA of a bucket = π(r₁ + r₂)l
= π(15 + 10) 13
= π × 25 × 13
TSA of a bucket

= π{25 × 13 + 225 + 100}
= π{325 + 325}
= 650π sq cm

Question 5.
From the top of a cone of base radius 24 cm and height 45 cm, a cone of slant height 45 cm, a cone of slant height 17 cm is cut off. What is the volume of the remaining frustum of cone.
Answer:

Question 6.
A vessel is in the form of a frustum of a cone. Its radius at one end is 8 cm and the height is 14 cm. If its volume is
\(\frac{5676}{3}\)cm³, find the radius of the other end.
Answer:


∴ Radius of the other end is 5 cm

Question 7.
A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones each of diameter 4\(\frac{2}{3}\)cm and height 3 cm. Find the number of cones so formed.
Answer:
Diameter of sphere = 28 cm,
radius = r₁ = \(\frac{28}{2}\) = 14cm


= 672 cones.

Question 8.
A petrol tank is in the shape of a cylinder with hemispheres of same radius attached to both ends. If the total length of the tank is 6m and the . radius is 1m, what is the capacity of the tank in litres.
Answer:

Radius of hemisphere = r = 1 m
Radius of cylinder = r = 1 m
height of the cylinder = 4 m
Capacity of the tank = volume of 2 hemispheres + volume of cylinder

= 16.7619 m³. [1 m = 100 cm]
= 16761900 cm³ [1000 cm³ = 1lit]
= \(\frac{16761900}{1000}\)
= 16761.9 litres.

Question 9.
A rocket is in the shape of a cylinder with a cone attached to one end and a hemisphere attached to the other end. All of them are the same radius of 1.5 m. The total length of the rocket is 7m and height of the cone is 2m. Calculate the volume of the rocket.
Answer:

Radius of the hemisphere and cylinder r = 1.5 m
height of cylinder = h = 7 – (2 + 1.5)
h = 3.5m
volume of Rocket = volume of hemisphere + volume of cone + volume of cylinder