Question

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Answer 1

Step-by-step explanation:

Question 1 :-

We Have :-

A Big Dome hemispherical in shape

To Find :-

Cloth material requured to cover the Big Dome

Formula Used :-

$csa \: of \: hemisphere \: = \: 2\pi {r}^{2}$

Solution :-

$csa \: of \: hemisphere \: = \: 2\pi {r}^{2} \\ \\ csa \: of \: hemisphere \: = \: 2\ \times \dfrac{22}{7} \times {( \dfrac{7}{2} )}^{2} \\ \\ csa \: of \: hemisphere \: = \: 2\ \times \dfrac{22}{7} \times \dfrac{49}{4} \\ \\ csa \: of \: hemisphere \: = \dfrac{2156}{28} \\ \\ csa \: of \: hemisphere \: = 77 \: {cm}^{2}$

Option A is the correct answer

Question 2 :-

We Have :-

Pillar ( cylinder + hemisphere )

To Find :-

Volume

Solution :-

$formula \: of \: volume \: of \: cylinder \: = \: \pi {r}^{2} h \\ \\ formula \: of \: volume \: of \: hemisphere \: = \: \dfrac{2}{3} \times \pi \times {r}^{3} \\ \\ volume \: of \: pillar \: = \: \pi {r}^{2} h + \dfrac{2}{3} \times \pi \times {r}^{3}$

Option D is the correct answer

Question 3 :-

We Have :-

Hemisphere with base radius 3 m

To Find :-

Volume

Formula Used :-

$volume \: of \: hemisphere \: = \: \dfrac{2}{3} \times \pi \times {r}^{3}$

Solution :-

$volume \: of \: hemisphere \: = \: \dfrac{2}{3} \times \pi \times {r}^{3} \\ \\ volume \: of \: hemisphere \: = \: \dfrac{2}{3} \times \ \dfrac{22}{7} \times {3}^{3} \\ \\ volume \: of \: hemisphere \: = \: \dfrac{1188}{21} \\ \\ volume \: of \: hemisphere \: = \:56.57 \: {m}^{3}$

Option C is the correcr answer

Question 4 :-

We Have :-

4 pillars

To Find :-

CSA of Pillars

Formula used :-

$csa \: of \: cylinder \: = \: 2 \: \pi \: r \: h \\ \\ csa \: of \: hemisphere \: = \: 2 \: \pi \: {r}^{2}$

Solution :-

$csa \: of \: pillar \: = \: 2 \: \pi \: r \: h \: + 2 \: \pi \: {r}^{2} \\ \\ csa \: of \: pillar \: = \: 2 \times \dfrac{22}{7} \times 2.5 \times 7.5 + 2 \times \dfrac{22}{7} \times 2.5 \times 2.5 \\ \\ csa \: of \: pillar \: = \: \dfrac{825}{7} + \frac{275}{7} \\ \\ csa \: of \: pillar \: = \: \dfrac{1100}{7} \\ \\ csa \: of \: pillar \: = \:157.14 \: {m}^{2} \\ \\ csa \: of \: 4 \: pillar \: = \:157.14 \times 4 \\ \\ csa \: of \:4 \: pillar \: = \:628.57 \: {m}^{2}$

Option D is the correct answer

Question 5 :-

We Have :-

Two Cylinder of height 2 cm and radius 1 cm

Sphere of radius 3 cm

To Find :-

Ratio

Formula Used :-

$volume \: of \: cylinder \: = \: \pi \: {r}^{2} \: h \\ \\ volume \: of \: sphere \: = \dfrac{4}{3} \: \pi \: {r}^{3}$

Solution :-

$volume \: of \: cylinder \: = \: \pi \: {r}^{2} \: h \\ \\ volume \: of \: sphere \: = \dfrac{4}{3} \: \pi \: {r}^{3} \\ \\ volume \: of \: cylinders \: = \: \dfrac{22}{7} \times 1 \times 1 \times 2 + \dfrac{22}{7} \times 1 \times 1 \times 2 \\ \\ volume \: = \: \dfrac{88}{7} \\ \\ volume \: of \: sphere \: = \: \dfrac{4}{3} \times \dfrac{22}{7} \times 3 \times 3 \times 3 \\ \\ volume \: = \: \dfrac{2376}{21} \\ \\ ratio \: = \: \dfrac{ \dfrac{88}{7} }{ \dfrac{2376}{21} } \\ \\ ratio \: = \: \dfrac{88 \times 21}{2376 \times 7} \\ \\ ratio = \dfrac{264}{2376} \\ \\ ratio \: = 1:9$

Answer 2

${\large{\sf{\pmb{\underline{About \; question...}}}}}$

★ A mathematics teacher took her grade X students to the Taj Mahal. It was an educational trip. She was interested in history also. On reaching there she told them about the history and facts about the seven wonder. She also told them that the structure of the moment is the combination of several solid figures. There are 4 pillars that are cylinderal in shape. A big dome in the centre and 2 more small domes on the both side of the big dome on its side. The domes are hemispherical. The pillars also have domes on them.

${\large{\sf{\pmb{\underline{Full \; Solution...}}}}}$

Question 1. How much cloth material will be required to cover a big dome of a diameter of 7 metres?

a. 77 m²

b. 78 m²

c. 79 m²

d. 80 m²

Answer 1. 77 m² is the cloth material will be required to cover a big dome of a diameter of 7 metres.

➟ Diameter = 7 m

➟ Surface area of hemisphere = 2πr²

➟ Radius = Diameter/2 = 7/2 = 3.5 m

~ Now we have to put values according to the using formula i.e., 2πr²

➟ 2πr²

➟ 2 × 3.14 × 3.5²

➟ 2 × 3.14 × 3.5 × 3.5

➟ 2 × 3.14 × 12.25

➟ 6.28 × 12.25

➟ 76.9300 (approx) Henceforth, 77 m²

Question 2. Write the formula to calculate the volume of the pillar.

Answer 2. As the pillar is in the shape of cylinder that's why here we have to use the formula to find volume of cylinder.

πr²h + 2/3πr³

Question 3. How much is the volume of the hemisphere if the radius of the base is 3 metres?

Answer 3. 56.57 m³ is the volume of the hemisphere if the radius of the base is 3 metres.

➟ 2/3 πr³

➟ 2/3 × 22/7 × 3³

➟ 2/3 × 22/7 × 27

➟ 44/21 × 27

➟ 56.57 m³

Question 4. Find the curved surface area of 4 pillars if the height of the pillar is 7.5 and the radius of the base is 2.5 m

Answer 4. is the curved surface area of 4 pillars if the height of the pillar is 7.5 and the radius of the base is 2.5 m

➟ 2πrh + 2πr²

➟ 2 × 22/7 × 2.5 × 7.5 + 2 × 22/7 × 2.5²

➟ 2 × 22/7 × 18.75 + 2 × 22/7 × 6.25

➟ 44/7 × 18.75 + 44/7 × 6.25

➟ 117.85 + 39.28

➟ 157.13 × 4

➟ 628.57 m²

Question 5. What is the ratio of the sum of the volumes of two cylinder of radius 1 cm and height 2 cm each to the radius of a sphere 3 cm.

Answer 5.

• Radius = 1 cm
• Height = 2 cm
• Radius = 2 cm

➟ V of cylinder = πr²h

➟ Volume of 2 cylinders = 2(22/7 × 1 × 1 ×2)

➟ V = 2(22/7×2)

➟ V = 2(44/7)

➟ V = 88/14

➟ Volume of sphere = 4/3 × π × r³

➟ V = 4/3 × 22/7 ×3³

➟ V = 4/3 × 22/7 × 27

➟ V = 88×9 / 7

➟ V = 792/7

➟ Ratio = (88/14)/(792/7)

➟ Ratio = 88 × 17/14 × 792

➟ Ratio = 1496/11088

➟ Ratio = 1/9

➟ Ratio = 1:9