A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm.
2007-02-23 23:43:34 · 5 answers · asked by Jenny 1 in Science & Mathematics ➔ Mathematics
I had a toy like that when I was a kid. Very boring thing to play with. I didn't like it at all. But, having it did help me with one thing. I got so bored playing with it, I actually did my own homework.
Long Live Jambi
2007-02-23 23:49:04 · answer #1 · answered by Anonymous · 1⤊ 0⤋
The height of the cone is 15.5 cm - 3.5cm = 12cm. The radius of the bottom of the cone is the same as the hemisphere = 3.5 cm. Plug these two numbers into the formula for the surface area of a cone, and do the same for the volume.
Since the cone is mounted on the hemisphere, you only have half a sphere. You only need to find the volume or surface area of a sphere with radius 3.5 cm and divide by 2.
Add the surface area of the cone to the surface area of the half sphere.
Add the volume of the cone to the volume of the half sphere
2007-02-23 23:59:24 · answer #2 · answered by Anonymous · 0⤊ 0⤋
First the hemisphere: surface area of a sphere is 4pi*r^2, so for a hemisphere it is half that,
2*pi*(3.5)^2
For the cone: you need to find the length from the apex to the edge. There is a right triangle with legs (15.5 - 3.5) = 12 and 3.5 (radius of the sphere). If you double these numbers you get 24 and 7, and might recognize that 7 24 25 is a pythagorean triple, so the length of the hypotenuse is 25/2.
Now for the surface area of the cone. For a circle with radius 25/2, the area is pi*(25/2)^2, and the circumference is 2*pi*25/2 = 25pi. The circumference of the circle at the base of the cone is the circumference of the hemisphere, 2*pi*3.5 = 7pi, so the ratio of the area of the pyramid surface to the full circle with radius 25/2 is 7pi/25pi = 7/25.
So, the total area is the sum of the two: 2*pi*(3.5)^2 + pi*(25/2)^2*(7/25)
2007-02-24 00:04:23 · answer #3 · answered by sofarsogood 5 · 0⤊ 0⤋
Volume of hemisphere = (2/3) Ï r ³ cm³
= (2/3) Ï x 3.5³ cm³ = 89.8 cm³
Height of cone = 12 cm
Volume of cone = (1/3)Ïr²h = (1/3)Ï x 3.5² x 12cm³ = 154cm³
Total volume = 243.8 cm³
Let slant height of cone = L
L² = 3.5² + 12²
L = 12.5cm
Surface area of cone = 1/2 ÏL²
= 0.5 x Ï x12.5 ² cm²
= 245.3 cm²
Surface area (curved) of hemisphere = 2/3Ïr²
= 2/3 x Ï x 3.5² cm² = 25.7cm²
Total surface area = 25.7 + 245.3 cm² = 271cm²
2007-02-24 00:43:32 · answer #4 · answered by Como 7 · 0⤊ 0⤋
The area for the hemisphere is 4 pi r sq/2 + area of cone.
area of cone is pi r l where r is 3.5 and l= sq root(r sq + 12sq)
Just calculate.If you wanna disuss it IM me at Jaagrut_live.
2007-02-24 00:17:23 · answer #5 · answered by Anonymous · 0⤊ 0⤋