English, asked by ishwarkoli254, 4 months ago

1. Two different words are joined to form a new word with a new meaning. Such
words are called Compound words. (Sometimes there is hyphen (-) between
compound words.)
For example : homework or kind-hearted
Pick out some Compound words from the lesson.
(1)
(3)
(4)
(5)
(6)
(2)​

Answers

Answered by sakshamgumber006
0

Answer:

GIVEN :-

A solid toy is in the form of a hemisphere surmounted by a right circular cone.

The height of the cone is 4 cm.

The diameter of the base is 8cm.

TO FIND :-

The volume of the toy.

If a cube circumscribes the toy, then find the difference of the volumes of the cube and the toy.

The total surface area of the toy.

Formula Used :-

\longmapsto \boxed{ \green{ \bf \: Volume_{(cone)} = \dfrac{1}{3} \pi \: {r}^{2}h }}⟼

Volume

(cone)

=

3

1

πr

2

h

\longmapsto \boxed{ \green{ \bf \:CSA_{(cone)} = \pi \: rl }}⟼

CSA

(cone)

=πrl

\longmapsto \boxed{ \green{ \bf \: Volume_{(hemisphere)} = \dfrac{2}{3} \pi \: {r}^{3} }}⟼

Volume

(hemisphere)

=

3

2

πr

3

\longmapsto \boxed{ \green{ \bf \: CSA_{(hemisphere)} = 2\pi \: {r}^{2} }}⟼

CSA

(hemisphere)

=2πr

2

\longmapsto \boxed{ \green{ \bf \:Volume_{(cube)} = {(side)}^{3} }}⟼

Volume

(cube)

=(side)

3

where,

r = radius

h = height of cone

l = slant height of cone

CALCULATION :-

1. VOLUME OF TOY

Given that

Radius of cone, r = 4 cm

Height of cone, h = 4 cm

Radius of hemisphere, r = 4 cm

So,

\pink{\rm :\implies\:Volume_{(toy)} = Volume_{(cone)} + Volume_{(hemisphere)}}:⟹Volume

(toy)

=Volume

(cone)

+Volume

(hemisphere)

\rm :\implies\:Volume_{(toy)} = \dfrac{1}{3} \pi \: {r}^{2}h + \dfrac{2}{3} \pi \: {r}^{3}:⟹Volume

(toy)

=

3

1

πr

2

h+

3

2

πr

3

\rm :\implies\:Volume_{(toy)} = \dfrac{1}{3} \pi \: {r}^{2}(h + 2r):⟹Volume

(toy)

=

3

1

πr

2

(h+2r)

\rm :\implies\:Volume_{(toy)} = \dfrac{1}{3} \times \dfrac{22}{7} \times {4}^{2} \times (4 + 8):⟹Volume

(toy)

=

3

1

×

7

22

×4

2

×(4+8)

\rm :\implies\:Volume_{(toy)} = \dfrac{1}{ \cancel3} \times \dfrac{22}{7} \times 16 \times \cancel{12} \: \: \: ^{4} :⟹Volume

(toy)

=

3

1

×

7

22

×16×

12

4

\rm :\implies\: \boxed{ \red{ \bf \: Volume_{(toy)} = \dfrac{1408}{7} \: {cm}^{3} }}:⟹

Volume

(toy)

=

7

1408

cm

3

2. SURFACE AREA OF TOY

Given that

Radius of cone, r = 4 cm

Height of cone, h = 4 cm

Radius of hemisphere, r = 4 cm

So,

Slant (l) height of cone is given by

\longmapsto \boxed{ \green{ \bf \: {l}^{2} = {h}^{2} + {r}^{2} }}⟼

l

2

=h

2

+r

2

\rm :\implies\: {l}^{2} = {4}^{2} + {4}^{2} :⟹l

2

=4

2

+4

2

\rm :\implies\: {l}^{2} = 16 + 16:⟹l

2

=16+16

\rm :\implies\: {l}^{2} = 32:⟹l

2

=32

\rm :\implies\:l = \sqrt{32} = 4 \sqrt{2} \: cm:⟹l=

32

=4

2

cm

\rm :\implies\:l \: = \: 4 \times 1.414:⟹l=4×1.414

\rm :\implies\:l \: = \: 5.656 \: cm:⟹l=5.656cm

Now,

Surface Area of toy is given by

\rm :\implies\: \pink{ \bf \: Surface Area_{(toy)} =CSA_{(cone)} + CSA_{(hemisphere)} }:⟹SurfaceArea

(toy)

=CSA

(cone)

+CSA

(hemisphere)

\rm :\implies\:Surface Area_{(toy)} = \pi \: rl \: + \: 2\pi \: {r}^{2} :⟹SurfaceArea

(toy)

=πrl+2πr

2

\rm :\implies\:Surface Area_{(toy)} = \pi \: r(l \: + \: 2r):⟹SurfaceArea

(toy)

=πr(l+2r)

\rm :\implies\:Surface Area_{(toy)} = \dfrac{22}{7} \times 4 \times (5.656 + 8):⟹SurfaceArea

(toy)

=

7

22

×4×(5.656+8)

\rm :\implies\:Surface Area_{(toy)} = \dfrac{22}{7} \times 4 \times 13.656:⟹SurfaceArea

(toy)

=

7

22

×4×13.656

\longmapsto \boxed{ \green{ \bf \:Surface Area_{(toy)} = 171.68 \: {cm}^{2} }}⟼

SurfaceArea

(toy)

=171.68cm

2

Now,

According to statement,

The toy is circumscribes by a cube.

So,

Edge of the cube = height of cone + height of hemisphere

So,

Edge of cube, x = 4 + 4 = 8 cm

\rm :\implies\: \pink{ \bf \: Volume_{(cube)} = {x}^{3} }:⟹Volume

(cube)

=x

3

\rm :\implies\:Volume_{(cube)} = {8}^{3} :⟹Volume

(cube)

=8

3

\longmapsto \boxed{ \green{ \bf \: Volume_{(cube)} = 512 \: {cm}^{3} }}⟼

Volume

(cube)

=512cm

3

Now,

Difference in the volume of cube and volume of toy is

\bull\purple{ \bf \: Volume_{(difference)} = Volume_{(cube)} - Volume_{(toy)}}∙Volume

(difference)

=Volume

(cube)

−Volume

(toy)

\rm :\implies\:Volume_{(difference)} =512 - \dfrac{1408}{7} :⟹Volume

(difference)

=512−

7

1408

\rm :\implies\:Volume_{(difference)} =\dfrac{3584 - 1408}{7} :⟹Volume

(difference)

=

7

3584−1408

\rm :\implies\:Volume_{(difference)} =\dfrac{2176}{7} :⟹Volume

(difference)

=

7

2176

\longmapsto \boxed{ \green{ \bf \:Volume_{(difference)} =310.86 \: {cm}^{3} }}⟼

Volume

(difference)

=310.86cm

3

Answered by Poojad6
0

Explanation:

1.sjkpkepdkdnkes

cuug9g9h9h0ju

Similar questions