A right circular cone is exactly fitted insid | vedclass

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

Question

(A) The volume of the cube is $V_{cube} = a^3 = 343 \, c.c.$Therefore,the edge length of the cube is $a = \sqrt[3]{343} = 7 \, cm$.Since the cone is f

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) The volume of the cube is $V_{cube} = a^3 = 343 \, c.c.$Therefore,the edge length of the cube is $a = \sqrt[3]{343} = 7 \, cm$.Since the cone is fitted inside the cube such that its base touches the edges of one face,the diameter of the base of the cone is equal to the side of the cube,$d = 7 \, cm$. Thus,the radius $r = 3.5 \, cm$.The height of the cone is equal to the side of the cube,$h = 7 \, cm$.The volume of the cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h$.$V_{cone} = \frac{1}{3} 	imes \frac{22}{7} 	imes (3.5)^2 	imes 7$.$V_{cone} = \frac{1}{3} 	imes 22 	imes 12.25 = \frac{269.5}{3} \approx 89.83 \, c.c.$Rounding to the nearest integer,the volume is approximately $90 \, c.c.$

Similar Questions

$A$ rectangular tin sheet is $12 \, cm$ long and $5 \, cm$ broad. It is rolled along its length to form a cylinder by making the opposite edges just touch each other. Then the volume of the cylinder is

If the radius of a cylinder is doubled and the height is halved,then what would be the ratio between the new curved surface area and the previous curved surface area of the cylinder?

If the volume of a sphere is numerically equal to its surface area,then its diameter is ......... $cm$.

$A$ plane divides a right circular cone into two parts of equal volume. If the plane is parallel to the base,then the ratio,in which the height of the cone is divided,is

The number of bricks,each measuring $25\,cm \times 12.5\,cm \times 7.5\,cm$,required to construct a wall $6\,m$ long,$5\,m$ high,and $0.5\,m$ thick,if the mortar occupies $5\%$ of the volume of the wall,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module