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

The capacity of a cylindrical tank is $246.4$ litres. If the height is $4$ metres,what is the diameter of the base? (in $m$)

If each side of a cube is increased by $10 \%$,the volume of the cube will increase by (in $\%$).

The material of a solid cone is converted into the shape of a solid cylinder of equal radius. If the height of the cylinder is $5\,cm$,then what is the height of the cone? (in $cm$)

$A$ cylindrical iron rod is $70\, cm$ long. The diameter of its end portion is $2\, cm$. What is its weight,reckoning a $cm^3$ of iron to weigh $10\, grams$? (in $kg$)

If the base radius of a cone is increased by $20 \%$ and its slant height is doubled,then by what percentage will the area of its curved surface increase?

Vedclass Test Series

Exam Paper Generator

Online Exam Module