Question

a cone of slant height 25cm has a curved surface area of 550 cm2. find the height of the cone and its volume

Answer 1

r = 22/7
r = ?
l = 25cm

CSA = π r l
550 = $\frac{22}{7}$ * r * 25
r = 550 * $\frac{7}{22}$ * $\frac{1}{25}$
r = 7 cm

h = √(l² - r²)
= √25² - 7²
= √625 - 49
= 24cm

V = πr²h
 =$\frac{1}{3}$ * $\frac{22}{7}$ * $7^{2}$ * 24
= 22 * 7 * 8
= 1232 $cm^{2}$

Answer 2

l = 25cm

CSA = 550 cm²
⇒ πrl = 550
⇒ r = (550×7)/(25×22)
⇒ r = 7cm

height, h = √(l² - r²) = √25² - 7² = √625 - 49 = √576 = 24cm

volume, V = $\frac{1}{3}$πr²h = $\frac{1}{3} \times \frac{22}{7} \times 7^2 \times 24=1232\ cm^2$