Question

A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy (use π =22/7)

Answer 1

Question :-

A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy . (use π =22/7)

Answer :-

$\bf{\underline\red{214.5\:cm}}$

Solution -

Total Surface Area = TSA

Curved Surfaces Area = CSA

TSA of toy = CSA of hemisphere + CSA of cone

Curved Surfaces Area of hemisphere

Radius of hemisphere = Radius of cone = r = 3.5 cm

➢ Curved Surfaces Area of Hemisphere = 2π r²

➪ 2 × 22/7 × ( 3.5 ) ²

➪ 2 × 22/7 × 3.5 × 3.5

➪ 2 × 22 × 0.5 × 3.5

➪ 77 cm²

➢ Curved Surfaces Area of Cone

curved surfaces area of cone = π r l

⠀ ⠀ ⠀ ⠀ ⠀ Radius of cone = r = 3.5 cm

Height of cone ➪ Total height of toy - radius of hemisphere

➪ 15 .5 - 3. 5

➪ 12 cm

Now , we find slant height (L)

we know that ,

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ L² = h² - r ²

➪ L² = (12)² + (3.5)²

${l}^{2} = ( {12})^{2} + { \frac{7}{2} }^{2}$

$= > {l}^{2} = 144 + \frac{49}{4}$

${l}^{2} = \frac{144 + 49}{4}$

${l}^{2} = \frac{144 \times 4 + 49}{4}$

${l}^{2} = \frac{576 + 49}{4}$

${l }^{2} = \: \frac{625}{4}$

${l}^{2} = \sqrt{ \frac{625}{4} }$

$l = \sqrt{ \frac{ {25}^{2} }{ {2}^{2} } }$

$l = \frac{25}{2}$

$l = 12.5 \: cm$

➢Curved Surfaces Area of cone = π r l

➪ 22/7 × 3.5 × 12.5

➪ 22 × 0.5 × 12.5

➪ 137 . 5 cm²

➢ TSA of toy = CSA of hemisphere + CSA of cone

⠀⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀➪ ( 77 + 137 . 5) cm²

⠀⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀➪ 214 . 5 cm²

━━━━━━━━━━━━━━━━━━━━━━━━━━

Hence , Total Surfaces Area of toy = $\bf{\underline\red{</strong><strong>2</strong><strong>1</strong><strong>4</strong><strong>.</strong><strong>5</strong><strong>cm</strong><strong>²</strong><strong>}}$

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Answer 2

Answer:

The total height of the toy is 15.5 cm .

Total surface area of toy = Curved Surface area of hemisphere + Curved Surface area of .on a hemisphere of radius 3.5 cm .

The total height of the toy is 15.5 cm .

Find the total surface area and volume of the toy .

Step-by-step explanation:

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