The given solid is a with a of 7 and a of 13.
Let's first calculate the surface and then the .
Surface Area
To calculate the , we can use the known formula where r is the radius of the base and l is the slant height of the cone.
S=Ï€ rl+Ï€ r^2By substituting 7 for r and 13 for l into the formula, we can calculate S.
S=Ï€ rl+Ï€ r^2
S=Ï€( 7)( 13)+Ï€( 7)^2
S=Ï€(7)( 13)+49Ï€
S=91Ï€+49Ï€
S=140Ï€
S=439.82297...
S≈ 439.82
The surface area of the cone is about 439.82 square meters.
Volume
To calculate the , we can use the following formula.
V= 13Ï€ r^2 h
Here, r is the radius and h is the height of the cone. We are given the radius of the cone but missing the height of the cone. From the figure, we can see a formed by the radius, the slant height, and the height of the cone.
We can use the to find the length of the longer leg of the triangle. Let's set c=13 and b= 7 and substitute these values in the Pythagorean formula.
c=a^2+b^2
13^2=a^2+ 7^2
169=a^2+49
120=a^2
± sqrt(120)=a
a=± sqrt(120)
We only need the positive value of the square root because height is a distance. Therefore, we have a cone with a height of sqrt(120) meters.
By substituting 7 for r and sqrt(120) for h into the formula, we can calculate V.
V=1/3Ï€ r^2 h
V=1/3Ï€ ( 7)^2 ( sqrt(120))
V=1/3Ï€(49)(sqrt(120))
V=1/349sqrt(120) π
V=49sqrt(120) π/3
V=562.10224...
V≈ 562.10
The volume of the cone is about 562.10 cubic meters.
