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A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is
Prepare for Class 10th Maths using NCERT solutions and MCQ-based questions from Chapter 12 Surface Areas and Volumes. Practice exercise questions short-answer problems and clear explanations to master concepts like surface areas and volumes of combinations of solids conversion of shapes and frustum of a cone. These resources are designed as per the CBSE syllabus for effective exam preparation. Consistent practice will sharpen your problem-solving skills and help you excel in board exams. Utilize step-by-step solutions and revision notes crafted to simplify learning and ensure success. Focus on understanding formulas and their applications to build a strong foundation. Begin solving now to achieve excellent results and secure higher marks in exams.
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Given:
– Total volume of solid = 3 × Volume of cone,
– Height of cone = h.
Volumes
– Volume of cone = (1/3)πr²h,
– Volume of cylinder = πr²H (H = height of cylinder),
– Total volume = Volume of cone + Volume of cylinder.
Equation for total volume
Total volume = 3 × Volume of cone:
(1/3)πr²h + πr²H = 3 × (1/3)πr²h.
Simplify:
πr²H = (3/3)πr²h – (1/3)πr²h,
πr²H = (2/3)πr²h.
Cancel πr²:
H = (2/3)h.
This question related to Chapter 12 Mathematics Class 10th NCERT. From the Chapter 12. Surface Areas and Volumes. Give answer according to your understanding.
For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-10/maths/
Given:
– Total volume of solid = 3 × Volume of cone,
– Height of cone = h.
Volumes
– Volume of cone = (1/3)πr²h,
– Volume of cylinder = πr²H (H = height of cylinder),
– Total volume = Volume of cone + Volume of cylinder.
Equation for total volume
Total volume = 3 × Volume of cone:
(1/3)πr²h + πr²H = 3 × (1/3)πr²h.
Simplify:
πr²H = (3/3)πr²h – (1/3)πr²h,
πr²H = (2/3)πr²h.
Cancel πr²:
H = (2/3)h.
For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-10/maths/