Question

A cone of maximum size is carved out from a cube of edge 28cm. find the surface area of the cone and of the remaining solid left out after the cone is carved out.
The first one to answer correctly will be marked as brainliest.

Answer 1

Given :-

• Edge of cube = 28cm.
• A cone of Maximum size is carved out from cube .

To Find :-

• Surface Area of cube ?
• Remaining Solid Left. ?

Formula & Concept used :-

• when a cone of Maximum size is Carved out from cube , Edge of cube is Equal to Diameter of cone and Height of cone .
• Slant Height of cone = √(H² + r²)
• Surface area of cone = π * radius * slant Height + πr²
• Total surface Area of cube = 6 * (side)²
• Radius = (Diameter)/2 .
• Surface area of remaining solid = Total surface area of cube - Area of circle where cone carved out + curved surface area of cone.

Solution :-

→ Edge of cube = Diameter & Height of cone = 28cm.

So,

→ Height of cone = 28cm.

→ Radius of cone = r = (28/2) = 14cm.

→ Slant Height of cone = l = √[(28)² + (14)²] = √(784 + 196) = √980 = 14√5 cm.

So,

→ surface Area of cone = π * r * l + πr²

→ Surface Area = [(22/7) * 14 * 14√5] + [ (22/7) * 14 * 14 ] = 616√5 + 616 = 616(√5 + 1) cm². -------- Equation (1)

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And,

→ Base Area of cone = πr²

→ Base Area = (22/7) * 14 * 14 = 616cm² ------- Equation (2)

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Now,

→ Total surface Area of cube = 6a²

→ TSA of cube = 6 * 28 * 28 = 4704cm². ------ Equation (3)

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Therefore ,

☛ Surface area of remaining solid = Total surface area of cube - Area of circle where cone carved out + curved surface area of cone.

Putting All values from Equation (1) , (2) & (3) Now, we get,

☛ Surface area of remaining solid = 4704 - 616 + [616(√5 + 1) ]

☛ Surface area of remaining solid = 4704 - 616 + 616 + 616√5

☛ Surface area of remaining solid = 4704 + 616√5

Putting √5 ≈ 2.23 Now,

☛ Surface area of remaining solid ≈ 4704 + 616*2.23

☛ Surface area of remaining solid ≈ 4704 + 1373.68

☛ Surface area of remaining solid ≈ 6077.68cm². (Ans.)

Hence, Surface area of remaining solid is 6077.68cm².

Answer 2

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$\huge\tt{GIVEN:}$

• A cone is carved out from a cube which is 28 cm

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$\huge\tt{TO~FIND:}$

• The surface area of cone and the remaining part of the cube.

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$\huge\tt{SOLUTION:}$

↪side of cube = diameter and height of the cone

↪ Height of the cone = 28 cm

↪ Diameter of cone = 28 & Radius would be 14 cm

↪Slant of cone would be = √[28²+14²]

↪√(784+196)

↪√980

↪14√5

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Then,

The surface area of cone = π×r×l+πr²

↪ Surface area of the cone = [{(22/7)×14×14√5}+{(22/7)×14×14}]

↪616√5+616

↪616(√5+1)cm² _____(EQ.1)

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↪Base area of cone = πr²

↪Base area = (22/7)×14²

↪616cm² ______(EQ.2)

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↪Total surface Area of cube = 6a²

→ TSA of cube =

↪ 6 × 28 ×28 = 4704cm²_____(EQ.3)

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Henceforth,

✡ Surface area of remaining solid = Total surface area of cube - Area of circle where cone carved out + curved surface area of cone.

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↪ Surface area of remaining solid = 4704 - 616 + [616(√5 + 1) ]

↪Surface area of the reaming solid = 4704 - 616 + 616 + 616√5

↪ Surface area of remaining solid = 4704 + 616√5

↪Surface area of remaining solid =4704 + 616×2.23

↪Surface area of remaining solid =4704 + 1373.68

↪Surface area of remaining solid =6077.68cm²

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