Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

The volume of a frustum of cone is calculated by using the formula ______.

A
$$\cfrac{1}{3}\pi h(R^2-r^2+Rr)$$

B
$$\cfrac{2}{3}\pi h(R^2+r^2+Rr)$$

C
$$\cfrac{2}{3}\pi h(R^2+r^2-Rr)$$

D
$$\cfrac{1}{3}\pi h(R^2+r^2+Rr)$$

Solution

V = volume
r = radius of the small circular end plane
R = radius of the big circular end plane
h = height of the frustum
$$\therefore \cfrac{1}{3}\pi h(R^2+r^2+Rr)$$
Question 2
1 / -0

The total surface area of a frustum of cone is calculated by using the formula _________.

A
$$2\pi[R^{2}+r^{2}+l(R+r)]$$

B
$$\pi[R^{2}+r^{2}+l(R+r)]$$

C
$$R^{2}+r^{2}+l(R+r)$$

D
$$\pi[R^{2}+r^{2}+l(R-r)]$$

Solution

Area of slanted surface$$=\pi l(r+R)$$
Area of base circle of frustum $$=\pi R^2$$

Area of top circle of frustum $$=\pi r^2$$

Total surface area $$=\pi[R^2+r^2+l(R+r)]$$
Question 3
1 / -0

Two cubes each of $$8cm$$ edge are joined end to end. Find the surface area of the resulting cuboid.

A
$$600cm^2$$

B
$$240cm^2$$

C
$$640cm^2$$

D
$$440cm^2$$

Solution

REF image:
Surface area = surface area of the cuboid having sides $$l,b,h$$ as $$(8+8)cm, 8cm, 8cm$$ respectively.
$$=2(lb+bh+hl)$$
$$=2((8+8)\times 8+8\times 8+(8+8)\times 8)$$

$$=2(128+64+128)$$

$$=640cm^{2}$$
Question 4
1 / -0

The curved surface area of frustum of a cone is given by

A
$$\pi(r_{1}+r_{2})l$$

B
$$\pi(r_{1}+r_{2})h$$

C
$$\pi(r_{1}-r_{2})l$$

D
$$\pi(r_{1}-r_{2})h$$

Solution
Question 5
1 / -0

The maximum length of a pencil that can be kept in rectangular box of dimensions $$12\ cm\times 9\ cm \times 8\ cm$$, is

A
$$13\ cm$$

B
$$17\ cm$$

C
$$18\ cm$$

D
$$19\ cm$$

Solution

Rectangular box is has the cuboidal shape. Maximum length of a pencil can be kept along the diagonal of the box.

We know that length of diagonal of the cuboid $$=\sqrt{l^2+b^2+h^2}$$
So,

$$D=\sqrt{12^2+9^2+8^2}$$

$$=\sqrt{144+81+64}$$

$$=17$$
Question 6
1 / -0

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is

A
6 cm

B
8cm

C
12 cm

D
24 cm

Solution

A metal sheet 27 cm long, 8 cm braod and 1 cm thick has the volume of = $$ 1\times b\times h $$ = $$ 27\times 8\times 1 $$ = 216 cm $$ ^{3} $$
As the sheet was melted to form a cube of edge length a, the volume of a cube = volume of the metal sheet
$$ \Rightarrow $$ $$ a^{3} $$ = $$ 216 cm^{3} $$
$$ \Rightarrow $$ a = 6 cm
Question 7
1 / -0

A cube of side 5 Cm is painted on all its faces. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their faces painted

A
27

B
42

C
54

D
142

Solution

(c) 54, Given , a cube of side 5 m is painted on all its faces and is sliced into 1 $$ Cm^{3} $$ cubes. Then, form figure, it is clear that there are 9 cubes available on face
As there are 6 faces, so the total number of smaller cubes = 6 x 9 = 54.
Question 8
1 / -0

A shuttle cock used for playing badminton has the shape of the combination of

A
a cylinder and a sphere

B
a cylinder and a hemisphere

C
a sphere and a cone

D
frustrum of a cone and a hemisphere

Solution

A shuttle cock used for playing badminton has the shape of the combination of frustrum of a cone and a hemisphere.
Question 9
1 / -0

A cylindrical pencil sharpened at one edge is the combinations of

A
a cone and a cylinder

B
frustrum of a cone and a cylinder

C
a hemisphere and a cylinder

D
two cylinders

Solution

The sharpened part of the pencil is cone and unsharpened part is cylinder.
Question 10
1 / -0

The radii of the top and bottom of a bucket of slant height $$45$$ cm are $$28$$ cm and $$7$$ cm respectively. The curved surface area of the bucket is

A
$$4950\ {cm}^{2}$$

B
$$4951\ {cm}^{2}$$

C
$$4952\ {cm}^{2}$$

D
$$4953\ {cm}^{2}$$

Solution

Given:
Slant Height, $$l = 45$$ cm
Top radius $$= 28$$ cm
Bottom radius $$=7$$ cm
Height $$=45$$ cm
Curved surface area $$=\pi l\left( r_1+r_2 \right) $$
$$=\dfrac { 22 }{ 7 } \times 45\left( 7+28 \right) $$
$$=4950 cm ^2$$