Volume of Hemisphere

Q.

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius.The radius of hemisphere is $3.5cm$ and the total wood used in the making of toy is 166$\frac{5}{6}c{m}^3$.Find the height of the toy.Also, find the cost of painting the hemispherical part of the toy at the rate of Rs.$10$ per $c{m}^2$.$(Take\pi =22/7)$

Q.

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $4cm$ and diameter of the base is $8cm$. Determine the volume of the toy. If a cube circumstances the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy.

Q. Question 9
An ice–cream cone full of ice cream having radius 5 cm and height 10 cm as shown I figure. Calculate the volume of ice- cream, provided that its $\frac{1}{6}$part is left unfilled with ice – cream.

Q. The volume of a hemisphere of radius r is ______ .

1. $\frac{1}{2}\pi r^2$
2. $\frac{2}{3}\pi r^2$
3. $\frac{1}{4}\pi r^3$
4. $\frac{2}{3}\pi r^3$

Q.

Question 9
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. Find the height of the cone.
(A) 12 cm
(B) 14 cm
(C) 15 cm
(D) 18 cm

Q.

If the total surface area of a solid hemisphere is $462c{m}^2$, find its volume.

Q. Question 6
From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Q.

A hemi-spherical tank is made up of an iron sheet $1cm$ thick. If the inner radius is$1m$, then find the volume of the iron used to make the tank. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Q.

A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in identical cones of height 12 cm and diameter 6 cm having a hemi-spherical shape on the top. Find the number of cones required.

Q. Question 1
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Q. A hemisphere dome, open at the base is made from a sheet of fibre. If the radius of the hemispherical dome is 40 cm and 13/170 of the fibre sheet was wasted in making the dome, then find the cost of the de at the rate of ₹ 35 per 100 cm^2.[Use π=3.14]

Q.

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

1. 144 cm³

2. 132 cm³

3. 154 cm³

4. 169 cm³

Q.

A cylinder, a cone and a hemisphere have equal base and equal height. What is the ratio in their volumes?

1. 1:02:03

2. 2:03:01

3. 3:01:02

4. 3:02:01

Q.

A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.

Q.

A solid toy in the form of a hemisphere surmounted by a right circular cone.Height of the cone is 2 cm and the diameter of the base is 4 cm.if a right circular cylinder circumstances the toy, find how much more space it will cover

Q.

A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of it, the volume of the solid.

Q.

Find the amount of water displaced by a solid spherical ball of diameter (Assume $\mathrm{\pi }=\frac{22}{7}$): $28cm$

Q. The curved surface area of a hemisphere is $308m^2$. Find the volume and the total surface area of the hemisphere.

1. $564m^3,432.997m^2$
2. $718.667m^3,462m^2$
3. $432.997m^3,564m^2$
4. $462m^3,718.667m^2$

Q.

If the volume of a hemisphere is four times its total surface area, what is its radius?

1. $21cm$

2. $12cm$

3. $9cm$

4. $18cm$

Q.

A solid right circular cylinder of radius 60 cm and height 20 cm is melted and recast into a right circular cone of height 3 times that of the cylinder. Find the curved surface area of the cone in square cm correct up to two places of decimal. $(Use\pi =3.14)$

Q. The volume of a hemisphere of radius r is ______ .

1. $\frac{1}{2}\pi r^2$
2. $\frac{2}{3}\pi r^2$
3. $\frac{1}{4}\pi r^3$
4. $\frac{2}{3}\pi r^3$

Q. A solid is in the form of the cone mounted on the hemisphere is such a way that the center of the base of the cone just coincide with the center of the base of the hemisphere .Slant height of the cone is L and radius of the base of the cone is 1/2 r , where r is the radius of the hemisphere .Prove that the total surface area of the solid is pi / 4 11r + 2l r square units.

Q. A hemispherical bowl of internal diameter 36 cm is filled with some liquid. This liquid is to be filled into Cylinder shaped bottles each of radius 3 cm and height 6 cm. Find the number of bottles required to empty the bowl.

1. 18
2. 72
3. 36
4. 154

Q.

A spherical lead ball of radius $10\mathrm{cm}$ is melted and small lead balls of radius $5\mathrm{mm}$ are made. The total number of possible small lead balls is

1. $800$

2. $125$

3. $400$

4. $8000$

Q.

The radius of a hemisphere having total surface area of 1848 sq. cm is 7 cm.

1. True

2. False

Q.

Find the volume of a hemisphere whose radius is $7cm$. (Given $\mathrm{\pi }=\frac{22}{7}$).

Q.

A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.

Q.

If the circumference of base of a hemisphere is $2\mathrm{\pi }$. Then what will be its volume

Q.

Find the amount of water displaced by a solid spherical ball of diameter $4.2cm$, when it is completely immersed in water.

Q.

An iron spherical ball of radius 21cm is melted and it is re casted in hemispherical balls of radius 7cm. How many such balls will be formed?

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