Get an answer in 5 minutes

We'll notify as soon as your question has been answered.

Plus iconAsk a question to our educators
MATHS
Asked by Amar

A solid hemisphere has a radius of x. A solid Cone has a diameter of 3x and a perpendicular height of y. the hemisphere and the cone have equal volumes. Show that y=8/9x. Use the formulas provided. Need help asap please!?

The volume of a cone is r^2(pi)h/3. The volume of a hemisphere is 2(pi)r^3/3 - this is found by dividing the volume of a sphere by 2. If the volumes of both shapes are equal, we can say: (1.5x)^2(pi)(y)/3 = 2(pi)(x^3)/3 We can get rid of the pi on both sides, and multiply both sides by 3 as well, to simplify the equation. y(1.5x)^2 = 2x^3 Expanding the left side’s brackets gives us: 2.25yx^2 = 2x^3 Solving for y gives us: y = 2/2.25 * x^3/x^2 y = 8/9 * x y = 8/9x as required Hope that helps, ~ Sohini

Sohini's profile picture
Verified
Sohini Khan
·

5.7k students helped

Similar Maths questions

What is Q&A on Scoodle?

At Scoodle we understand that everyone learns in a different way. Some people learn through practice, using essays and notes; others prefer video lessons to watch and learn, some just need help with a specifically hard question, while some learn best 1-on-1 tutoring sessions. At Scoodle we cater for all types of learning styles and needs. From GCSE Maths video lessons to A-level English essays and specialist educators in every subject - we’ve got you covered.

Faces of students on ScoodleFaces of students on ScoodleFaces of students on Scoodle
Scoodle has helped over 131,000 students so far

5 Maths tutors available now

Need help with Maths?

Getting expert help from a tutor is a great way to improve your Maths grades.

Badge showing the text 'New'Discover learning resources by tutors

Learn Maths with Video Lessons
GCSE Maths - Numbers
1hr 28m · 8 videos
Paja's profile picture
Paja Kruzikova
·

696 students helped

GCSE Maths - Numbers
Quadratic Inequalities
28m · 3 videos
Iqbal's profile picture
Iqbal Lokman
·

1.5k students helped

Quadratic Inequalities
GCSE Maths - Ratios
1hr 32m · 9 videos
Paja's profile picture
Paja Kruzikova
·

696 students helped

GCSE Maths - Ratios
GCSE Maths - Algebra A
56m · 6 videos
Paja's profile picture
Paja Kruzikova
·

696 students helped

GCSE Maths - Algebra A
GCSE Maths - Algebra B
1hr 14m · 7 videos
Paja's profile picture
Paja Kruzikova
·

696 students helped

GCSE Maths - Algebra B
GCSE Maths - Algebra C
1hr 27m · 9 videos
Paja's profile picture
Paja Kruzikova
·

696 students helped

GCSE Maths - Algebra C