Surface Area of Combined Solids

Q.

As observed from the top of a $75\mathrm{m}$ high lighthouse from the sea level, the angles of the depression of the two ships are $30°$ and $45°$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Q.

There is a solid cylinder of base radius 5 cm and height 10 cm. From one of the flat ends of the solid cylinder a hemispherical depression having same radius as cylinder is hollowed out. What is the total surface area (in sq.cm) of this new solid?

1. 175$\pi$

2. 75$\pi$

3. 100$\pi$

4. 120$\pi$

Q.

There is a solid cylinder of base radius 5 cm and height 10 cm. From one of the flat ends of the solid cylinder a hemispherical depression having same radius as cylinder is hollowed out. What is the total surface area (in sq.cm) of this new solid?

Q. An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion be 8 cm and the diameter of the top of the funnel be 18 cm, then find the area of the tin sheet required to make the funnel.

$\left[3\right]$

Q. Draw a tangent at any point $R$ on a circle of radius $3.2cm$ and centre $P$.

Q. Draw a circle with centre O and radius 3.5 cm. Draw two tangents PA and PB from an external point P such that $<APB={45}^0$. What is the value of $<AOB+<APB$.

Q.

A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, is surmounted by a cone of equal base and height 2.8 m. Find the cost of canvas required for making the tent at ₹100 per sq.m.

1. ₹ 6590

2. ₹ 7590

3. ₹ 8590

4. ₹ 9876

Q.

There is a cylinder of base radius 3 cm and length 10 cm. Ram attaches a hemispherical attachment to each flat end of the cylinder having the same radius as the base radius of the cylinder. What is the surface area of the combined solid in $c{m}^2$ ?

1. 302

2. 310

3. 400

4. 201

Q.

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter as that of cylinder is hollowed out. Find the total surface area of the remaining solid. $(Use\pi =\frac{22}{7})$

1. $19.60{\text{cm}}^2$

2. $18.60{\text{cm}}^2$

3. $17.60{\text{cm}}^2$

4. $15.60{\text{cm}}^2$

Q. In a circle of radius $4cm$, draw two radii such that the angle between them is ${120}^o$. Draw two tangents at the ends of the radii.

Q. Take a circle with centre $C$ and construct a tangent to a circle from an external point $P$.

Q. Draw a circle of suitable radius and draw chord XY of length $4.6$ cm. Draw tangents at point X and point Y.

Q.

There is a cylinder of base radius 3 cm and length 10 cm. Ram attaches a hemispherical attachment to each flat end of the cylinder having the same radius as the base radius of the cylinder. What is the surface area of the combined solid in $c{m}^2$ ?

1. 310

2. 201

3. 400

4. 302

Q. Draw a circle of diameter 7 cm and construct tangents at the ends of a diameter.

Q. From a point on the ground $40m$ away from the foot of a tower, the angle of elevation of the top of the tower is ${30}^o.$ The angle of elevation of the top of a water tank (on the top of the tower) is ${45}^o.$
Find the height of the tower

Q. Draw a circle of radius $4.2$ cm. Draw a pair of tangents to this circle inclined to each other at an angle of ${45}^0$.;

Q. The surface area of the solid of hemispherical base of radius 7 cm surmounted by cone of slant height 7 cm is ____.

1. 462 cm${}^2$
2. 221 cm${}^2$
3. 262 cm${}^2$
4. 421 cm${}^2$