A cone has a height of #12 cm# and its base has a radius of #15 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is #1500.5(1dp)# sq.cm

The cone is cut at 3 cm from base, So upper radius of the frustum of cone is #r_2=(12-3)/12*15=11.25#cm ; slant ht #l=sqrt(3^2+(15-11.25)^2)=sqrt(9+14.0625)=sqrt 23.0625=4.80#cm
Top surface area #A_t=pi*11.25^2=397.61# sq.cm Bottom surface area #A_b=pi*15^2=706.858# sq.cm Slant Area #A_s=pi*l*(r_1+r_2)=pi*4.80*(15+11.25)=396.03# sq.cm
Total surface area of bottom segment #=A_t+A_b+A_s=397.61+706.86+396.03=1500.5(1dp)#sq.cm[Ans]
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the surface area of the bottom segment of the cone after it's cut 3 cm from the base, we first need to calculate the slant height of the smaller cone formed by the cut. Using the Pythagorean theorem, we can find the slant height ( l ) of the smaller cone:

[ l = \sqrt{r^2 + h^2} ] [ l = \sqrt{15^2 + (12 - 3)^2} ] [ l = \sqrt{225 + 81} ] [ l = \sqrt{306} ] [ l ≈ 17.49 \text{ cm} ]

Now, we can calculate the lateral surface area of the smaller cone, which is the surface area of the bottom segment:

[ A = πr'l ] [ A = π(15)(17.49) ] [ A ≈ 2617.12 \text{ cm}^2 ]

Therefore, the surface area of the bottom segment of the cone after it's cut 3 cm from the base is approximately ( 2617.12 \text{ cm}^2 ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7