# Free Surface Areas and Volumes 02 Practice Test - 9th Grade

The cost of painting the curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹ 10/- per sq. meter is ₹ 2200/-.
(use π=227)

A.

True

B.

False

#### SOLUTION

Solution : A

Curved surface area of the cylindrical pillar
=2πrh
=2×227×3.5×10
=220 m2

So,
total cost of painting
=Curved Surface Area of pillar×Cost per m2
=220×10
= ₹ 2200/-

Hence, the given statement is true.

The radius of a hemisphere having total surface area of 1848 sq. cm is 7 cm.

A.

True

B.

False

#### SOLUTION

Solution : B

Total surface area =3πr2

3×227×r2=1848

r2=1848×73×22

r2=196

r=14 cm

Thus, above statement is false.

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice should she prepare?

A.

35 L

B.

42.5 L

C.

38.5 L

D.

50 L

#### SOLUTION

Solution : C

We know that,
Volume of a cylindrical container
=πr2h

1000 cm3=1 L

Hence, the volume of each cylindrical tumbler
=227×72×10

=1540 cm3

So, the total volume of juice required
=1540×25
=38500 cm3
= 38.5 L

The ratio of the radius to the height of a right cone is 3:4. Then the ratio of total surface area to curved surface of the cone is____.

A.

2:3

B.

3:5

C.

7:9

D.

8:5

#### SOLUTION

Solution : D

Given that,
r:h = 3:4
Let r = 3x and h = 4x

From the relation
l2=h2+r2,

The Slant height:
l=(3x)2+(4x)2
l=5x

We know that,
Total surface area of cone
=πr(r+l)
Curved surface area of cone
=πrl

Hence, the required ratio
=Total surface area of coneCurved surface area

=πr(r+l)πrl

=π×3x(3x+5x)π×3x×5x

=8:5

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of the pillar to that of dome is 4:3, then what is the ratio of their volumes?

A.

2:1

B.

3:1

C.

4:1

D.

1:1

#### SOLUTION

Solution : C

Given that, the ratio of the height of the pillar to that of dome is 4:3 .

hcylinderhcone=43

We know that,
volume of cylinder=πr2h.
volume of cone=13πr2h.

Now, ratio of  volume of cylinder to the volume of cone
=πr2hcylinder13πr2hcone

=πr2×413πr2×3

=41

=4:1

The total surface area in m2 of a cuboid with dimensions of 26m, 14m and 6.5m respectively is ___ m2.

#### SOLUTION

Solution :

Total Surface Area = 2( l x b + b x h + h x l)
= 2(26 x
14 + 14 x 6.5 + 6.5 x 26)
= 2(364 + 91 + 169
=1248 m2

There is a conical tent whose slant height is 14 m. If the curved surface area of cone is 308 m2,  then its base area is _______.

A.

132 m2

B.

224 m2

C.

254 m2

D.

154 m2

#### SOLUTION

Solution : D

The curved surface area of a cone = πrl
where, r is radius and l is slant height.

308=πrl
227×r×14=308
r=308×722×14
r=7 m

Base area
=πr2
=227×72
=154 m2

The water in a cubical tank of side 10m is transferred to completely fill a cuboidal tank of length 5m and breadth 10 and height h. Then the height of the cuboidal tank (in metres) is ___

#### SOLUTION

Solution :

Volume of cube = ​(side)3

Volume of cuboid = (length) × (breadth) × (height)

So height of cuboidal tank can be found by equating the two

height=side3length×breadth

=1035×10

Height = 20m

An iron spherical ball of radius 21cm is melted and it is re-casted in hemispheres of radius 7cm. The number of balls formed will be

___

#### SOLUTION

Solution :

The volume will remain constant.

Let's assume x such hemispherical balls will be formed.

So  43πR3=x23πr3

(Where R is the radius of spherical ball and r is the radius of the hemispheres)

43π(21)3=x23π(7)3

x=2×21×21×217×7×7
x=54

The volume of a cylinder is 231 cm3 and its height is 6 cm. A ball will fit inside the cylinder if its radius is ______.

A.

3 cm

B.

cm

C.

2.5 cm

D.

cm

#### SOLUTION

Solution : A and C

Volume of cylinder =π×r2×h
231=227×r2×6
r2=231×722×16
r2=12.25
r=3.5
So, a ball will fit inside the cylinder if its radius is less than or equal to 3.5 cm.