The radius of a right circular cylinder and a hemisphere is equal and their volumes are also equal. The height of the hemisphere is greater than the height of the cylinder by
(a) 25%
(b) 50%
(c) 100%
(d) 200%
WBBSE
Class X
Mathematics
Real Life Problems Related To Different Solid Object
01 Mark
2025
(b) 50%
Explanation:
- Volume of a cylinder = πr²h
- Volume of a hemisphere = 2\over 3πr³
Given both volumes are equal, we get:
πr²h = 2\over 3πr³
Solving for h:
h = 2\over 3 r
Now, the height of the hemisphere is r.
The increase in height:
r – 2\over 3r = 1\over 3r
Percentage increase:
1\over 3 ÷ 2\over 3 × 100 = 50%
Related Questions
More WBBSE Moderate level questions
1/12
Q.
If the height and base area of a solid hemisphere and a solid cylinder are...
A.
(b) 1 : 2 Explanation: Let radius = r. For hemisphere: height...
Q.
The lower part of an ice-cream is conical and upper part is hemispheric with same...
A.
Cone height (h) = 9 cm, base radius (r) = 2.5 cm...
Q.
The shape of a pencil with one end sharpened is the combination of a and...
A.
Cone and Cylinder
Q.
Find the ratio of the volumes of a solid right circular cylinder and a solid...
A.
Volume of circular cylinder = πr²h or, Volume of cone = πr²h...
Q.
Find the ratio of length of radius and perimeter of a circle
A.
The perimeter (circumference) of a circle is given by: C = 2Ï€r...
Q.
If the roots of a quadratic equation ax² + bx + c = 0 (a...
A.
Let the roots be α and -1/α. Product of roots: r ×...
Q.
If 0° < θ < 90° then sin θ < sin²θ.
A.
False Explanation: We know that for 0° < θ < 90°, 0...
Q.
In a joint business one of the two friends invests ₹ xyz for y months...
A.
False Explanation: Profit is distributed in the ratio of the product of...
Q.
If x(4 – √3) = y(4 + √3) = 1, then the value of x²...
A.
4 Explanation: x = 1 and y = 1 Solving for x...
Q.
27, 31, 46, 52, x, y + 2, 71, 79, 85, 90 are in increasing...
A.
(d) 126 Explanation: n = 10 (even) median = or, 64 =...
Q.
If a : 2 = b : 5 then how many % of b is...
A.
(c) 40 Explanation: ⇒ a / 2 = b / 5 ⇒...
Q.
Find x, if sin x = cos (x – 20°)
A.
cos (x - 20°) = sin x cos (x - 20°) =...