The base of a cone with radius 6 , cm and hei | vedclass

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

Question

(A) Given: Radius of cone and hemisphere $r = 6 \, cm$,Height of cone $h = 8 \, cm$. First,find the slant height $l$ of the cone: $l = \sqrt{r^2 + h^2

Vedclass · Accepted Answer

$414.48 \, cm^2, 753.6 \, cm^3$

Vedclass · Answer

(A) Given: Radius of cone and hemisphere $r = 6 \, cm$,Height of cone $h = 8 \, cm$. First,find the slant height $l$ of the cone: $l = \sqrt{r^2 + h^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, cm$. Curved Surface Area $(CSA)$ of the solid = $CSA$ of cone + $CSA$ of hemisphere. $CSA$ = $\pi rl + 2\pi r^2 = \pi r(l + 2r) = 3.14 	imes 6 	imes (10 + 2 	imes 6) = 18.84 	imes (10 + 12) = 18.84 	imes 22 = 414.48 \, cm^2$. Volume of the solid = Volume of cone + Volume of hemisphere. Volume = $\frac{1}{3}\pi r^2h + \frac{2}{3}\pi r^3 = \frac{1}{3}\pi r^2(h + 2r) = \frac{1}{3} 	imes 3.14 	imes 6^2 	imes (8 + 2 	imes 6) = \frac{1}{3} 	imes 3.14 	imes 36 	imes (8 + 12) = 3.14 	imes 12 	imes 20 = 37.68 	imes 20 = 753.6 \, cm^3$.

The base of a cone with radius $6 \, cm$ and height $8 \, cm$ is hemispherical. Find the curved surface area and the volume of the solid. $(\pi = 3.14)$

Similar Questions

Write 'True' or 'False' and justify your answer:
Two identical solid cubes of side $a$ are joined end to end. Then the total surface area of the resulting cuboid is $12 a^{2}$.

$A$ metallic sphere of radius $21 \,cm$ is melted and recast to form a wire with diameter $0.5 \,cm$. Find the length of the wire in $m$.

$A$ container is in the form of a cylinder closed at one end by a hemisphere. The radius of the cylinder is $8.4 \,cm$ and the total height of the container is $52.8 \,cm$. How many litres of petrol can this container hold? (in $litres$)

The surface area of a sphere with radius $7\,cm$ is $\ldots \ldots \ldots \ldots cm ^{2}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module