Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the volume of a right circular cone that has a height of 11.7 in and a base with a circumference of 18.8in. Round your answer to the nearest tenth of a cubic inch. Answer: in ^(3)

Find the volume of a right circular cone that has a height of 1111.77 in\text{in} and a base with a circumference of 18.8 18.8 in\mathrm{in} . Round your answer to the nearest tenth of a cubic inch.\newlineAnswer: in\text{in} 3 ^{3}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 6right chevron icon
Evaluate variable expressions: word problemsright chevron icon

Full solution

Q. Find the volume of a right circular cone that has a height of 1111.77 in\text{in} and a base with a circumference of 18.8 18.8 in\mathrm{in} . Round your answer to the nearest tenth of a cubic inch.\newlineAnswer: in\text{in} 3 ^{3}
  1. Find Radius of Base: First, we need to find the radius of the base of the cone. The formula for the circumference of a circle is C=2πrC = 2\pi r, where CC is the circumference and rr is the radius. We can rearrange this formula to solve for rr: r=C2πr = \frac{C}{2\pi}.
  2. Calculate Radius: Now, let's calculate the radius using the given circumference of 18.818.8 inches: r=18.8 in2πr = \frac{18.8 \, \text{in}}{2\pi}. We can approximate π\pi as 3.141593.14159.
  3. Calculate Volume Formula: Performing the calculation: r=18.8 in2×3.14159r = \frac{18.8 \, \text{in}}{2 \times 3.14159} ≈18.8 in6.28318≈2.993 in\approx \frac{18.8 \, \text{in}}{6.28318} \approx 2.993 \, \text{in}. This is the radius of the base of the cone.
  4. Plug in Values: Next, we use the formula for the volume of a cone, which is V=(13)πr2hV = (\frac{1}{3})\pi r^2 h, where VV is the volume, rr is the radius, and hh is the height.
  5. Calculate Volume: We plug in the values for rr and hh into the volume formula: V=13π(2.993 in)2(11.7 in)V = \frac{1}{3}\pi(2.993 \, \text{in})^2(11.7 \, \text{in}).
  6. Square Radius: Now, we calculate the volume: V=(13)×3.14159×(2.993 in)2×11.7 inV = (\frac{1}{3}) \times 3.14159 \times (2.993 \text{ in})^2 \times 11.7 \text{ in}.
  7. Multiply by Height and π\pi: First, square the radius: (2.993 in)2≈8.958 in2(2.993 \, \text{in})^2 \approx 8.958 \, \text{in}^2.
  8. Round the Answer: Then, multiply by the height and π\pi: V≈(1/3)×3.14159×8.958 in2×11.7 in≈3.14159×2.986 in2×11.7 in≈104.187 in3V \approx (1/3) \times 3.14159 \times 8.958 \text{ in}^2 \times 11.7 \text{ in} \approx 3.14159 \times 2.986 \text{ in}^2 \times 11.7 \text{ in} \approx 104.187 \text{ in}^3.
  9. Round the Answer: Then, multiply by the height and π\pi: V≈(1/3)×3.14159×8.958 in2×11.7 in≈3.14159×2.986 in2×11.7 in≈104.187 in3V \approx (1/3) \times 3.14159 \times 8.958 \text{ in}^2 \times 11.7 \text{ in} \approx 3.14159 \times 2.986 \text{ in}^2 \times 11.7 \text{ in} \approx 104.187 \text{ in}^3. Finally, we round the answer to the nearest tenth: V≈104.2 in3V \approx 104.2 \text{ in}^3.

More problems from Evaluate variable expressions: word problems

Question
Evaluate the expression for j=7 j = 7 .\newline2j= 2j = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Evaluate the expression for y=4 y = 4 and z=5 z = 5 . \newline yz= yz = _____
Get tutor helpright-arrow

Posted 7 months ago

Question
Evaluate the expression for t=0 t = 0 .\newline∣−4−t∣=|-4 - t| = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Dale drew 88 pictures. Belle drew pp fewer pictures than Dale. Choose the expression that shows how many pictures Belle drew. \newlineChoices: \newline(A) 88\newline(B) p−8p - 8\newline(C) 8+p8 + p\newline(D) 8−p8 - p
Get tutor helpright-arrow

Posted 9 months ago

Question
Write an expression for the sequence of operations described below. subtract 55 from 66, then add ww to the result Do not simplify any part of the expression. ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Write an expression for the operation described below. \newlinesubtract 44 from aa \newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
John baked 1212 cookies. Alice baked nn fewer cookies than John.\newline Choose the expression that shows how many cookies Alice baked.\newline Choices:\newline(A) 1212\newline(B) n−12n - 12\newline(C) 12+n12 + n\newline(D) 12−n12 - n
Get tutor helpright-arrow

Posted 9 months ago

Question
Emma read 1515 books. Lucas read bb fewer books than Emma. Choose the expression that shows how many books Lucas read.\newlineChoices:\newline(A) 1515\newline(B) b−15b - 15\newline(C) 15+b15 + b\newline(D) 15−b15 - b
Get tutor helpright-arrow

Posted 10 months ago

Question
Max ran 1010 miles. Sarah ran mm fewer miles than Max. Choose the expression that shows how many miles Sarah ran.\newlineChoices:\newline(A)10(A)10\newline(B)m−10(B)m - 10\newline(C)10+m(C)10 + m\newline(D)10−m(D)10 - m
Get tutor helpright-arrow

Posted 9 months ago

Question
Carlos wrote 2020 poems. Fiona wrote pp fewer poems than Carlos. Choose the expression that shows how many poems Fiona wrote.\newlineChoices:\newline(A) 2020\newline(B) p−20p - 20\newline(C) 20+p20 + p\newline(D) 20−p20 - p
Get tutor helpright-arrow

Posted 10 months ago

View all (114)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant