Question

Find the surface area and the volume of the figure
Round to the nearest tenth if needed.

Answer 1

> V = 217.68 cm³

> S = 227.14 cm²

Explanation:

We are required to find the surface area and the volume of the given figure . This question is from Combination of solids . As we can see that this figure is made up of a cuboid and cylinder.

Firstly let's find out the volume .

> V = V_( cuboid) + V_(cylinder)

> V = 9cm × 4cm × 5cm + π × ( 2cm)²× 3cm

> V = 180 cm³ + 3.14 × 4cm² × 3cm

> V = 180 cm³ + 37.68 cm³

> V = 217.68 cm³

Lets find the surface area :-

> S = S_( cuboid) + S_( cylinder) - πr²

> S = 2( 9×4 + 4× 5 + 5×9) cm² + 2×π×2cm × 3cm - 3.14 × (2cm)²

> S = 239.7 cm² - 12.56 cm²

> S = 227.14 cm²

Note :-

• Here we subtracted πr² from the total surface area of cuboid and cylinder because that much area of the cuboid was covered by the base of the cylinder .

Answer 2

• See below

Explanation:

Surface area:

• S = 2(lw + lh + wh) + 2πrh
• S = 2(9*4 + 9*5 + 4*5) + 2*3.14*2*3 = 239.7 cm² (rounded)

Volume:

• V = lwh + πr²h
• V = 9*4*5 + 3.14*2²*3 = 217.7 cm³ (rounded)