Chef Potato's body has a cylinder in the middle and two half spheres that make up his bottom and head. He has the two dimensional shape measurements as follows: 20 cm in total length, 5 cm between the end of the cylinder and the top of the top sphere. Reduce Chef1.) Potato by a scale factor of 0.5.2.) Chef Potato needs to be converted from a two dimensional shape to a three dimensional object and then enlarged to 300% of his original size. The three dimensional chef potato is similar in shape to a capsule made of a half sphere at the top, and a half sphere at the bottom and a cylinder in between. Determine the surface area of the enlarged three dimensional chef potato and the scale factor.3.) What are possible dimensions of a box that could be used to deliver the enlarge model of chef potato to store? Justify your answer.
4 years ago
Answered By Emily D
That is a lot of question all at once! Let's try to break it down a bit.
Chef Potayto is a cylinder with a rounded top and bottom (so his total size is 1 sphere + 1 cylinder).
The cylinder is 20cm tall and the sphere has a radius of 5 cm ("5 cm between the end of the cylinder and the top of the sphere"). How I got a radius of 5cm from that sentence is easier to understand if you draw out Chef Potahto.
I tried my best to draw him out below. My tablet isn't plugged in so it's more of a Picasso piece than a realistic rendering. Pretend that squoval is a circle and we're good.
To scale him by a factor of 0.5, we just multiply all the dimensions by 0.5
$5\times0.5=2.5$5×0.5=2.5
$20\times0.5=10$20×0.5=10
300% of original size, which was 100%
$\frac{300\%}{100\%}=3$300%100% =3 so we multiply the original dimensions by 3
$5\times3=15$5×3=15
$20\times3=60$20×3=60
Now to calculate the surface area
The surface area of a sphere is $4\pi r^2=4\pi\left(15\right)^2$4πr2=4π(15)2
The surface area of the cylinder is $2\pi rh=2\pi\left(15\right)\left(60\right)$2πrh=2π(15)(60)
This is WITHOUT the top and bottom of the cylinder or bottoms of half-spheres, both of which are covered because they're touching (so they don't count as surface area).
$A_{Total}=2\pi\left(15\right)\left(60\right)+4\pi\left(15\right)^2$ATotal=2π(15)(60)+4π(15)2
The total surface area of Chef Potayto is 8482.3 cm2 or 0.85 m2
Looking at our Super Awesome Drawing of Chef Potahto (and tripling all the numbers) we know we'd need a box that is about 30cm x 30cm x 90cm
Attached Whiteboard:
Play Drawing