Question

A circular cone has a height of 17 mm and a slant
height of 21 mm. Find
(i) the volume,
(ii) the total surface area,
of the cone.
please answer me fast its urgent​

Answer 1

• Given

h = 17mm , l = 21mm

• Solution

slant height (l²) = h² + r²

21² = 17² + r²

441 = 289 + r²

r² = 441 - 289

r² = 152

r = 12.32mm

i. volume of cone = 1/3 π r²h

= 1/3 × π × 152 × 17 ......{r² = 152}

= 50.6 π × 17

= 861.33 π mm³

volume of cone is 861.33 π mm³

ii. total surface area of cone = πr(r + l)

= 12.32 π ( 12.32 + 21)

= 12.32 π (33.32)

= 410.50 π mm²

Total surface area of cone = 410.50 π mm²

Answer 2

Given :-

• A circular cone has a height of 17 mm and a slant height of 21 mm.

To find :-

• Volume and total surface area of circular cone

Solution :-

• Slant height of cone = 21 mm

• Height of cone = 17 mm

As we know that

→ Slant height = √(radius)² + (height)²

→ l = √r² + h²

→ 21 = √r² + (17)²

→ 21 = √r² + 289

Squaring both side

→ 441 = r² + 289

→ r² = 441 - 289

→ r² = 152

→ r = √152 = 12.3 mm

Now, volume of cone

→ ⅓ πr²h

→ ⅓ × π × 12.3 × 12.3 × 17

→ π × 4.1 × 12.3 × 17

→ π × 50.43 × 17

→ 857.31π mm³

Total surface area of cone

→ πrl + πr²

→ πr(l + r)

→ π × 12.3(21 + 12.3)

→ 12.3π × 33.3

→ 409.59π mm²

Hence,

• Volume of cone is 857.31π mm³

• Total surface area of cone is 409.59π mm²