Chapter 12.3, Problem 6CE

To determine

To calculate: The lateral area, total area, and volume of the cone.

Answer to Problem 6CE

5. l =5 cm, lateral area = 47.1 sq.cm, total area = 75.36 sq.cm, and volume = 37.68 cu.cm

6. r = 5 cm, lateral area = 204.1 sq.cm, total area = 282.6 sq.cm, volume = 314 cu.cm

7. h = 8 cm, lateral area = 188.4 sq.cm, total area = 301.44 sq.cm, volume = 301.44 cu.cm

Explanation of Solution

Given information: Consider the given information,

5. Radius = 3 cm, Height = 4 cm

6.Height = 12 cm, Length = 13 cm

7.Radius = 6 cm, Length = 10 cm

  $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height, l = length

  $l=\sqrt{{(r)}^2+{(h)}^2}$

  $r=\sqrt{{(l)}^2-{(h)}^2}$

  $h=\sqrt{{(l)}^2-{(r)}^2}$

Lateral area = $\pi rl$

Total area = $\pi rl+\pi r^2$

Volume = $\frac{1}{3}\pi r^{2}h$

Calculation : Consider the given information the formula is,

5. $l=\sqrt{{(3)}^2+{(4)}^2}=\sqrt{25}=5$ cm

Lateral area = $3.14\times 3\times 5=47.1$ sq.cm

Total area = $(3.14\times 3\times 5)+(3.14\times {(3)}^2)=75.36$ sq.cm

Volume = $\frac{1}{3}\times 3.14\times {(3)}^2\times 4=37.68$ cu. cm

6. $r=\sqrt{{(13)}^2-{(12)}^2}=\sqrt{25}=5$ cm

Lateral area = $3.14\times 13\times 5=204.1$ sq.cm

Total area = $(3.14\times 5\times 13)+(3.14\times {(5)}^2)=282.6$ sq.cm

Volume = $\frac{1}{3}\times 3.14\times {(5)}^2\times 12=314$ cu.cm

7. $h=\sqrt{{(10)}^2-{(6)}^2}=\sqrt{64}=8$ cm

Lateral area = $3.14\times 6\times 10=188.4$ sq.cm

Total area = $(3.14\times 6\times 10)+(3.14\times {(6)}^2)=301.44$ sq.cm

Volume = $\frac{1}{3}\times 3.14\times {(6)}^2\times 8=314$ cu.cm