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 3.5 cm 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 4 cm and diameter of the base is 8 cm.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 462 $c{m}^2$, 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.

A cylindrical water flask has a hemispherical cap which exactly fits on the flask. The height and radius of the flask are 20 cm and 3 cm respectively. If the cap is used as the cup to drink water, how many cups of water can be served.

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