The radii of five metal spheres are 1, cm, 3, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) $1$. Volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. $2$. Total volume of the five spheres = $\frac{4}{3}\pi (1^3 + 3^3 + 4^3 + 5^3 + 8^3

Vedclass · Accepted Answer

$9\, cm, 27$

Vedclass · Answer

(A) $1$. Volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. $2$. Total volume of the five spheres = $\frac{4}{3}\pi (1^3 + 3^3 + 4^3 + 5^3 + 8^3) = \frac{4}{3}\pi (1 + 27 + 64 + 125 + 512) = \frac{4}{3}\pi (729)$. $3$. Let the radius of the new large sphere be $R$. Then $\frac{4}{3}\pi R^3 = \frac{4}{3}\pi (729)$,which implies $R^3 = 729$,so $R = 9\, cm$. $4$. Volume of one cylinder = $\pi r^2 h = \pi (3^2)(4) = 36\pi\, cm^3$. $5$. Number of cylinders = $\frac{	ext{Total Volume}}{	ext{Volume of one cylinder}} = \frac{\frac{4}{3}\pi (729)}{36\pi} = \frac{972\pi}{36\pi} = 27$ cylinders.

Similar Questions

The edges of three of the four cubes are $1\, cm, 9\, cm$ and $10\, cm$ respectively. If the total volume of two cubes with $9\, cm$ edge and $10\, cm$ edge is equal to the volume of the remaining two cubes,find the edge of the fourth cube in $cm$.

The diameter of a solid hemisphere is $7 \, cm$. Find its curved surface area and total surface area (in $cm^2$).

The radius and slant height of a cone are in the ratio of $5:13$. If its curved surface area is $1836.9 \, cm^2$,find its volume. (Use $\pi = 3.14$) (in $cm^3$)

The length of the longest pole that can be placed in a room of dimensions $(10 \text{ m} \times 10 \text{ m} \times 5 \text{ m})$ is (in $\text{m}$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module