find the volume of each cone. round to the nearest tenth. (example 1)
1.
2.
3 height: 8.4 feet
diameter: 3.5 feet
4. height: 3.9 yards
radius: 1.7 yards
5. a party hat like the one at the right is going to be filled with candy.
what is the volume of the hat? round to the nearest tenth. (example 2)
6. mr. walthour is building a storage shed in a conical shape. the base
of the shed is 4 meters in diameter and the height of the shed is
3.8 meters. what is the volume of the shed? round to the nearest
tenth. (example 2)
find the volume of each solid. round to the nearest tenth. (example 3)
7.
8.

Question

find the volume of each cone. round to the nearest tenth. (example 1)
1.
2.
3 height: 8.4 feet
diameter: 3.5 feet
4. height: 3.9 yards
   radius: 1.7 yards
5. a party hat like the one at the right is going to be filled with candy.
   what is the volume of the hat? round to the nearest tenth. (example 2)
6. mr. walthour is building a storage shed in a conical shape. the base
   of the shed is 4 meters in diameter and the height of the shed is
   3.8 meters. what is the volume of the shed? round to the nearest
   tenth. (example 2)
find the volume of each solid. round to the nearest tenth. (example 3)
7.
8.

Accepted Answer

### Problem 1: Find the volume of the cone with slant height 23 mm and radius 14 mm (assuming the 14 mm is radius, and we need to find height first)
# Explanation:
## Step 1: Find the height of the cone
We know the slant height $ l = 23 $ mm, radius $ r = 14 $ mm. Using the Pythagorean theorem for a cone $ h=\sqrt{l^{2}-r^{2}} $
$ h=\sqrt{23^{2}-14^{2}}=\sqrt{529 - 196}=\sqrt{333}\approx18.25 $ mm
## Step 2: Use the volume formula for a cone $ V=\frac{1}{3}\pi r^{2}h $
$ V=\frac{1}{3}\times\pi\times14^{2}\times18.25 $
$ V=\frac{1}{3}\times\pi\times196\times18.25 $
$ V=\frac{1}{3}\times\pi\times3577 $
$ V\approx\frac{1}{3}\times3.1416\times3577\approx3757.3 $ cubic mm (rounded to nearest tenth)
# Answer:
$ \approx3757.3 $ cubic mm

### Problem 2: Cone with radius 1.1 ft and slant height 3.8 ft (find height first)
# Explanation:
## Step 1: Find the height
$ h = \sqrt{l^{2}-r^{2}}=\sqrt{3.8^{2}-1.1^{2}}=\sqrt{14.44 - 1.21}=\sqrt{13.23}\approx3.64 $ ft
## Step 2: Volume of cone $ V=\frac{1}{3}\pi r^{2}h $
$ V=\frac{1}{3}\times\pi\times1.1^{2}\times3.64 $
$ V=\frac{1}{3}\times\pi\times1.21\times3.64 $
$ V=\frac{1}{3}\times\pi\times4.4044 $
$ V\approx\frac{1}{3}\times3.1416\times4.4044\approx4.6 $ cubic ft (rounded to nearest tenth)
# Answer:
$ \approx4.6 $ cubic ft

### Problem 3: Cone with height 8.4 ft and diameter 3.5 ft (radius = diameter/2 = 1.75 ft)
# Explanation:
## Step 1: Identify radius and height
$ r=\frac{3.5}{2}=1.75 $ ft, $ h = 8.4 $ ft
## Step 2: Volume of cone $ V=\frac{1}{3}\pi r^{2}h $
$ V=\frac{1}{3}\times\pi\times1.75^{2}\times8.4 $
$ V=\frac{1}{3}\times\pi\times3.0625\times8.4 $
$ V=\frac{1}{3}\times\pi\times25.725 $
$ V\approx\frac{1}{3}\times3.1416\times25.725\approx26.9 $ cubic ft (rounded to nearest tenth)
# Answer:
$ \approx26.9 $ cubic ft

### Problem 4: Cone with height 3.9 yards and radius 1.7 yards
# Explanation:
## Step 1: Use volume formula for cone $ V=\frac{1}{3}\pi r^{2}h $
$ V=\frac{1}{3}\times\pi\times1.7^{2}\times3.9 $
$ V=\frac{1}{3}\times\pi\times2.89\times3.9 $
$ V=\frac{1}{3}\times\pi\times11.271 $
$ V\approx\frac{1}{3}\times3.1416\times11.271\approx11.8 $ cubic yards (rounded to nearest tenth)
# Answer:
$ \approx11.8 $ cubic yards

### Problem 5: Party hat (cone) with diameter 7 in (radius = 3.5 in) and height 8 in
# Explanation:
## Step 1: Identify radius and height
$ r=\frac{7}{2}=3.5 $ in, $ h = 8 $ in
## Step 2: Volume of cone $ V=\frac{1}{3}\pi r^{2}h $
$ V=\frac{1}{3}\times\pi\times3.5^{2}\times8 $
$ V=\frac{1}{3}\times\pi\times12.25\times8 $
$ V=\frac{1}{3}\times\pi\times98 $
$ V\approx\frac{1}{3}\times3.1416\times98\approx102.6 $ cubic inches (rounded to nearest tenth)
# Answer:
$ \approx102.6 $ cubic inches

### Problem 6: Conical shed with diameter 4 m (radius = 2 m) and height 3.8 m
# Explanation:
## Step 1: Identify radius and height
$ r=\frac{4}{2}=2 $ m, $ h = 3.8 $ m
## Step 2: Volume of cone $ V=\frac{1}{3}\pi r^{2}h $
$ V=\frac{1}{3}\times\pi\times2^{2}\times3.8 $
$ V=\frac{1}{3}\times\pi\times4\times3.8 $
$ V=\frac{1}{3}\times\pi\times15.2 $
$ V\approx\frac{1}{3}\times3.1416\times15.2\approx15.9 $ cubic meters (rounded to nearest tenth)
# Answer:
$ \approx15.9 $ cubic meters

### Problem 7: Two cones (frustum - like but two cones) with upper cone radius 8 cm, height 16 cm and lower cone radius 8 cm, height 8 cm
# Explanation:
## Step 1: Volume of upper cone $ V_1=\frac{1}{3}\pi r^{2}h_1 $
$ V_1=\frac{1}{3}\times\pi\times8^{2}\times16=\frac{1}{3}\times\pi\times64\times16=\frac{1024}{3}\pi $
## Step 2: Volume of lower cone $ V_2=\frac{1}{3}\pi r^{2}h_2 $
$ V_2=\frac{1}{3}\times\pi\times8^{2}\times8=\frac{512}{3}\pi $
## Step 3: Total volume $ V = V_1+V_2=\frac{1024 + 512}{3}\pi=\frac{1536}{3}\pi = 512\pi\approx1608.5 $ cubic cm (rounded to nearest tenth)
# Answer:
$ \approx1608.5 $ cubic cm

### Problem 8: Composite solid (cylinder + cone) with cylinder radius 6 cm, height 8.5 cm and cone radius 6 cm, height 10 cm
# Explanation:
## Step 1: Volume of cylinder $ V_{cylinder}=\pi r^{2}h_{cylinder} $
$ V_{cylinder}=\pi\times6^{2}\times8.5=\pi\times36\times8.5 = 306\pi $
## Step 2: Volume of cone $ V_{cone}=\frac{1}{3}\pi r^{2}h_{cone} $
$ V_{cone}=\frac{1}{3}\times\pi\times6^{2}\times10=\frac{1}{3}\times\pi\times36\times10 = 120\pi $
## Step 3: Total volume $ V = V_{cylinder}+V_{cone}=306\pi+120\pi = 426\pi\approx1338.2 $ cubic cm (rounded to nearest tenth)
# Answer:
$ \approx1338.2 $ cubic cm

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QUESTION IMAGE

Question

Explanation:

Problem 1: Find the volume of the cone with slant height 23 mm and radius 14 mm (assuming the 14 mm is radius, and we need to find height first)

Step 1: Find the height of the cone

Step 2: Use the volume formula for a cone \( V=\frac{1}{3}\pi r^{2}h \)

Step 1: Find the height

Step 2: Volume of cone \( V=\frac{1}{3}\pi r^{2}h \)

Step 1: Identify radius and height

Step 2: Volume of cone \( V=\frac{1}{3}\pi r^{2}h \)

Answer:

Problem 2: Cone with radius 1.1 ft and slant height 3.8 ft (find height first)