[tex]\bf \textit{lateral surface of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} ~~ r=radius\\ sh=\stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=3.5\\ sh=6.5 \end{cases}\\\\\\ LA=\pi (3.5)(6.5)\implies LA\approx71.47 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{sh}{6.5}=\sqrt{r^2+h^2}\implies 6.5=\sqrt{3.5^2+h^2}\implies 6.5^2=3.5^2+h^2 \\\\\\ 6.5^2-3.5^2=h^2\implies \sqrt{6.5^2-3.5^2}=h\implies \sqrt{30}=h \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3.5\\ h=\sqrt{30} \end{cases}\implies V=\cfrac{\pi (3.5)^2\sqrt{30}}{3}\implies V\approx 70.26[/tex]
Answer to Q1:
A = 71.47 sq.ft
Step-by-step explanation:
We have given the base radius and the slant height of the cone.
base radius = r = 3.5 feet and slant height = √r²+ h² = 6.5 feet
We have to find the lateral surface area of the cone.
The formula to find the lateral surface area of the cone:
A = πr√r²+h²
Putting values in above formula, we have
A = π(3.5)(6.3)
A = 71.47 sq.ft which is the answer.
Answer to Q2:
V = 70.26 cubic ft
Step-by-step explanation:
We have given the base radius and the slant height of the cone.
base radius = r = 3.5 feet and slant height = √r²+h² = 6.5 feet
We have to find the volume of the cone.
The formula to find the lateral surface area of the cone:
V = πr²h / 3
√r²+h² = 6.5
√3.5²+h² = 6.5
h = √30
Putting values in above formula, we have
V = π(3.5)²(√30) / 3
V = π (12.25)√30 / 3
V = 70.26 cubic ft which is the answer.
